In what was a scrappy affair, it took until the 64th minute for the deadlock to be broken as Jack Cork's initial effort crossed the line following a mix-up between Trippier and Tom Heaton.
The Swans had star man Lukas Fabianski, who kept out a late Sam Vokes effort, to thank for ensuring that Garry Monk's men picked up back-to-back wins for just the third time this season.
Relive how the action unfolded with Sports Mole's live text coverage below.
The hosts are in desperate need of points as they look to claw their way out of the relegation zone, while City are focusing on cementing their position in the top half of the table. It has been an inconsistent start to the year for Garry Monk's charges, which will give Burnley plenty of confidence heading into this afternoon's meeting.
Sean Dyche has named an unchanged side once more this afternoon following on from last weekend's battling draw against league leaders Chelsea. The Clarets boss certainly likes sticking with a small group of players, and having seen Ashley Barnes escape punishment for his challenge on Nemanja Matic seven days ago (you may have read about it through the week), it is the same starting lineup for the home side who could really do with three points this afternoon.
Kevin Long and Dean Marney remain on the treatment table and are unlikely to feature again this season, so it looks like a classic 4-4-2 formation laid out by Dyche with Barnes supporting top scorer Danny Ings up top. Kieran Trippier and Ben Mee will provide some width from their full-back positions, while the now familiar midfield four offer a mixture of grit and creativity.
As far as Swansea are concerned, it's just the one change from last weekend's impressive victory against Manchester United. Tom Carroll has been introduced in place of Gylfi Sigurdsson, who misses out on the trip to Lancashire due to a slight hamstring problem. That is a real blow for the Swans ahead of kickoff, with their most creative player failing to make the squad.
Other than the Sigurdsson blow, Monk has no fresh injury concerns for this one. Some expected Jefferson Montero to come back into the side to offer some width, but the Swansea boss clearly did not want to change too much on the back of that win against Man United. A big afternoon for Tottenham Hotspur academy product Carroll, then, who lines up in a midfield five alongside Jack Cork, Jonjo Shelvey, Sung-Yeung Ki and Wayne Routledge.
As already mentioned, Montero has to make do with a place among the Swansea subs this afternoon, and he is joined by fellow attacking threats Nelson Oliveira and Marvin Emnes among the visiting side's backups. Burnley can call upon Sam Vokes from the bench should they need to, while Lukas Jutkiewicz and Ross Wallace are also part of the matchday squad.
So it's a big day ahead for Burnley, then, who come into this game on the back of a mixed bag of results in recent times. Draws away at Chelsea and Manchester City certainly stick out, but defeats against Crystal Palace and Sunderland, combined with another draw at West Bromwich Albion, ensures that they still remain inside the Premier League's bottom three. That can all change with a positive result here today, however, with the Clarets currently sitting level on points with Queens Park Rangers in 17th place.
The division remains extremely tight at the bottom, with Aston Villa, Burnley, Queens Park Rangers and Sunderland all separated by just three points, and in fact anyone from Everton down in 12th place could still face the drop. There is a tough run of fixtures ahead for Burnley, though, with this their easiest game until mid-April - on paper, at least.
That is because after today Dyche's men must take on Liverpool, Manchester City, Southampton, Tottenham Hotspur and Arsenal in successive games, so anything less than three points against Swansea really could leave them in big danger. As things stand, however, survival is still a real possibility for the Clarets, despite having won just four games all term - three of them coming at Turf Moor.
Of course, all the talk in the build-up to this one has been about last week's meeting against Chelsea, with the 2-2 scoreline going somewhat under the radar. It's pointless dwelling on what happened regarding Barnes and Matic, but it will be interesting to see how the former Brighton & Hove Albion man responds here today. We saw a real battling and determined display from Burnley at Stamford Bridge, and if they can match that against the Swans then there is no reason why they can't claim all three points in front of their home supporters.
Similarly, Swansea have had a mixed bag of results since the turn of the year, dropping points against sides you would expect them to beat - Sunderland, Queens Park Rangers - although their triumph against an in-form Man United last time out has put a nice shine on recent displays. Relegation is certainly out of the question for the Welsh outfit now, even if they are three points short of the magic 40 mark, with the only real motivation being to surpass their previous highest Premier League tally.
The Swans currently have 37 points to their name, meaning that they are well on course to surge beyond their previous best of 47 from back in their maiden Premier League campaign in 2011. As well as that victory over United, there was also a classic away performance at Southampton, remember, which highlights that Monk's charges are inside the top half of the Premier League on merit rather than luck. Tottenham Hotspur and Liverpool await in the next week, but even with those tough fixtures on the horizon you would back Swansea to cement their position inside the top 10.
Worryingly for Swansea, they have scored just five goal in their last six games since prolific forward Wilfried Bony jumped ship to Man City, but that didn't seem to hold them back too much when they put two past David de Gea last Saturday. There is no denying that they are the league's most inconsistent side, though, winning seven, drawing seven and losing seven of their last 21 games in the top flight.
DID YOU KNOW? Burnley have conceded 44 goals in the Premier League so far this season - the second worst record behind fellow strugglers QPR (45). Swansea have dropped a mammoth 16 points from winning positions, meanwhile, which is the division's second highest tally in that particular department.
PREVIOUS MEETINGS: These two sides have met on just one previous occasion in the top flight, Swansea running out 1-0 winners when they faced off in South Wales earlier this season. That means that victory here today will see them pull off their first double over the Clarets since way back in the 1932-33 campaign. If history is anything to go by then it will be a tough ask, however, as they have won on just two of their past 22 league and cup visits to Turf Moor, losing 13 of those games.
City have an impressive record against teams in the bottom half this season having lost just one of their last 13 against those placed between 11th-20th. Six draws in that run just goes to highlight once more how inconsistent they have been, though, with plenty of incentive there for Burnley to go on and win this one.
The game's early kickoff between West Ham United and Crystal Palace at Upton Park finished in a 3-1 away win, meaning that Palace are now eight points clear of the relegation zone. It seems that Alan Pardew has turned them from near-certainties for the drop at one stage into a side battling to join Swansea in midtable. QPR and Leicester don't play this weekend, incidentally, while Aston Villa take on Pardew's former club Newcastle.
PREDICTION: Looking at this one logically, a solid midtable side up against a team inside the relegation zone, you would only really back one side if your life depended on it. The Premier League works in mysterious ways, though, and up against a Swansea side who have made an inconsistent start to 2015, Burnley will surely have earmarked this afternoon's match as a contest that they simply have to win with a horrible run of fixtures coming up. 2-1.
Well they are my thoughts, but what about the Sports Mole Sofa team? There's still a couple of minutes to check out their preview ahead of this Premier League clash:
KICKOFF! We're underway at Turf Moor with Burnley, in their traditional claret and blue strip, kicking from left to right. Can they push on from last week's impressive draw against Chelsea and pick up the points needed to climb out of the league's bottom three? Let's find out.
The home side have seen more of the ball in the early stages without really causing any danger in the attacking third. Swansea are perhaps happy to sit back in the early stages and invite their opponents onto them before breaking forward.
SHOT! Routledge swings in the first cross of the afternoon into a decent area, but there is nobody in a white shirt anywhere to be seen. Up the other end Boyd makes the most of a loose ball on the edge of the box, turning and firing away a shot to test Fabianski with a simple stop in the end.
Burnley continue their positive start to the game as Boyd uses his strength to burst into the box, although he lost control of the ball before getting a shot away. He felt as though he was tugged back a little by Naughton, but there was absolutely no chance referee Jonathan Moss was going to award a penalty for that.
Swansea have seen more of the ball over the past few minutes, but Burnley will not be too concerned as the visitors are failing to push into advanced areas of the field. It is the Clarets who have made the better start to the contest, with Boyd's shot the closest we have come to a goal so far.
Some good play from Boyd, the game's best player in these early stages, paves the way for Kightly to win his side a corner which Gomis clears away. That led to City springing a counter-attack, but the move broke down when Ki's pass went astray on the edge of the box.
A strange 30 seconds of play as Mee scuffs a clearance inside his own area, which landed right to the feet of Shelvey. The former Liverpool midfielder stumbled on the ball, though, before eventually winning it back and horribly over-hitting a cross.
Burnley have edged out Swansea in terms of possession so far 58%-42%. There's not been a great deal to shout about in terms of chances for either side inside the opening 15, as this game struggles to truly ignite.
Swansea's travelling supporters are in good voice at the moment, as are the home spectators, but things on the field remain scrappy and somewhat flat. A lot of the game is being played in midfield as the two sides continue to cancel each other out.
Routledge bursts into the box and looks to behind Burnley's backline, but Keane superbly tracks back and tackles the flying winger to concede a corner. That was a fine challenge from the former Manchester United defender, which he had to time to perfection.
Trippier swings a superb cross into the box, right into the zone where you would expect a player in claret and blue to be gambling. In the end the ball was cleared behind for another corner, which once more came to nothing.
SAVE! Unquestionably the best moment of the game so far at Turf Moor, as Fabianksi pulls off a fine reaction save to deny Barnes. Ings created the opening with an unorthodox flick to take Fernandez out of the game, but his teammate couldn't get the better of the Swans stopper from a few yards out.
CHANCE! This match has sprung to life at long last. It's now Swansea's turn to come close to opening the scoring as Routledge latches onto Shelvey's superb ball over the top, although he failed to find the target when lofting the ball over the out-rushing Tom Heaton. Routledge wanted a penalty, claiming that Heaton clipped him before he got his shot away, and he does have a point. That would have been a harsh decision had Jonathan Moss pointed to the spot, though.
The visiting side are probing away at the moment, knocking the ball around in midfield before slowly edging forward, but Burnley are remaining tight at the back to plug up any gaps.
SAVE! Fabianski is called into action again, this time denying Kightly at the end of his mazy run into the box. Good play from the hosts, but they must be careful because Swansea are looking good on the counter.
It's just not happening for the Swans at the moment, as another attack breaks down. Gomis has really struggled to get into the game, with the visitors' only real opening of the game so far falling to Routledge a short while ago. Both teams looking fairly lively, but the end product is lacking.
The atmosphere has good awfully flat which perfectly matches events on the field. I expected Burnley to really get in their opponents' faces, but that has not really been the case. They have looked the better side, yet a goal is not exactly merited.
Both sides continue to give the ball away rather cheaply with the deadlock yet to be broken. It's been a half of very few chances, and I wouldn't be surprised if it remained this way until the interval.
CHANCE! A brilliant chance goes begging for Swansea striker Bafetimbi Gomis. Having timed his run well to get in behind the Burnley backline, the Frenchman opted for power rather than placement and fired well over the bar from the edge of the box when in on goal. That came just moments after he had tested Heaton with a tame effort from a similar distance following the stopper's weak clearance.
Swansea looking the stronger side at the moment following that decent spell. Gomis has been on the periphery for the last 38 minutes or so, but he could - and perhaps should - have given the Welsh outfit a slender lead prior to the break.
Both sides win free kicks within crossing range of the box, but a mixture of poor crossing and bad movement sees the set pieces come to nothing. One minute to go until the half-time interval.
CLOSE! Shelvey and Routledge link up brilliantly in the attacking third of the pitch, with the former working some space on the edge of the box to curl an effort narrowly wide of Heaton's goal. The visitors looking by far the stronger side at the end of the opening 45 minutes.
Referee Jonathan Moss brings the first half to a close, and in truth it has not been the greatest advert for Premier League football. Chances have been few and far between in a game contested between two sides who have done well to cancel each other out for large parts.
Burnley certainly had the better of things in the opening quarter of the game, testing Fabianski on a couple of occasions with Barnes's shot the closest they came to finding a way through. Swansea grew into the game and ended the half as the better side, as Shelvey and Gomis both came close to breaking the deadlock.
The only other chance of note fell the way of Routledge on 26 minutes, although he could not find the target after lifting the ball over Heaton. It has been an evenly-balanced affair on the whole, but hopefully the best from both sides is still yet to come.
A reminder of the options available to both managers at the break should they wish to change things around slightly. Both Sean Dyche and Garry Monk are likely to wait until the hour mark before taking any action, you feel, as they look to see how the early stages of the second half play out.
Elsewhere in the Premier League this afternoon, Aston Villa trail 1-0 against Newcastle United, while West Brom lead Southampton by the same scoreline. It means that Burnley will end the day outside the bottom three as things stand, with Swansea remaining in ninth place.
SECOND HALF UNDERWAY! A big 45 minutes ahead for Burnley, then, as play resumes in Lancashire. No changes at the break as the home side look to attack from the off.
The windy conditions are certainly not making things easy at Turf Moor, which may go some way to explaining the number of wayward, overhit passes. This second period has started the same way as the first with Burnley seeing more of the ball.
Swansea have really missed Gylfi Sigurdson this afternoon, with a real lack of creativity in midfield. Which manager will move first and make a change?
Williams is lucky to escape a booking after catching Ings in the face with his elbow. The Clarets were unable to punish the visitors from the resulting free kick, which lacked the quality needed once again.
Kightly does well to win the ball but he runs into trouble with teammates better placed than him inside the box. The danger wasn't fully dealt with by Swansea, although Arfield's shot from the edge of the box actually ended up going out for a throw-in.
PENALTY APPEAL! Burnley players strongly appeal for a penalty after Kightly's flick appeared to come back off the hand of Fernandez. The Clarets are just turning the screw slightly, but a goal still seems a million miles away at the moment.
Neither keeper has been tested as much as they should have as we approach the hour mark. We will surely see a few changes in the next few minutes because as things stand this game is destined for the graveyard slot on Match of the Day. It's not been a classic.
Montero has taken his warm-up gear off on the touchline and looks certain to enter the fray shortly. Nathan Dyer is not in the squad for the second game running this afternoon, so the Ecuadorian is needed to provide some width.
CLOSE! Some great play by Trippier down the right leads to Barnes receiving the ball in a central position inside the box. His first touch set him up perfectly to fire away a volley towards goal, which missed the target by a few inches. Fabianski looked to have had it covered anyway, but a decent attempt nonetheless.
SWANSEA CITY SUB: As expected, Montero replaces Carroll as Monk makes the first alteration of the afternoon. Will that make a difference? Swansea supporters will certainly hope so because their side have not offered enough in attack over the last hour.
It's a cruel blow for former Cardiff City keeper Tom Heaton, who pulled off a wonder save to deny the Swans before seeing the ball crawl over the line. A corner into box was fired towards goal by Cork from a few yards out, but Heaton somehow touched it onto the bar. Then a scramble ensued, Trippier slashing at the ball which Heaton seemed to carry over the line. One of the strangest goals you are likely to see, which is pretty relevant for this scrappy contest.
Having seen the replay of that goal six or seven times, I still can't quite work out what on earth happened! It's certainly an own goal, but whether it's Heaton or Trippier who is credited with it will be left to the dubious goals panel to decide.
Swansea's opener has gone down as a Kieran Trippier own goal. It's Burnley 0-1 Swansea after 71 mins #BURSWA
— Premier League (@premierleague) February 28, 2015
Neither side have really done enough to merit holding the lead, but credit to Swansea for digging deep to find a way through. Still 18 minutes remaining for Burnley to find a response, but since falling behind they've done little to rectify the situation.
BURNLEY SUB: Sam Vokes replaces Kightly as we enter the final 15 minutes of the game, meaning that Burnley essentially have three forwards on the field now. It's all or nothing for the relegation-threatened side.
Burnley have seen a lot of the ball in the last few minutes without truly troubling the Swans defence. They really need to up things now if they are to rescue a point, and their best chance of doing so seems to be through Trippier's driving runs down the flank.
The visitors are struggling to get out of their own half at the moment, as Burnley look to test the opposition with a few set pieces which fail to bring any chances. Trippier's latest cross into the box was dangerous, but it sailed over the heads of his teammates who were waiting at the back post.
Ings, who has been awfully quiet on the whole this afternoon, looked to be in one-on-one with Fabianski only for the linesman's flag to go up on the far side for offside. Replays show that the correct call was made.
SAVE! Fabianski has been the busier of the two keepers today, and he needed to be alert to keep hold of Barnes' curled effort from 20 yards out. A decent attempt as Burnley continue to push forward.
Another penalty appeal is turned down for Burnley, although in fairness these calls were fairly muted. Vokes and Taylor had a hold of each other inside the box, but the referee felt that it was six of one and waved play on.
SAVE! Fantastic save from Fabianski, who has arguably been the game's best performer this afternoon. Vokes did well to turn a cross towards goal, and it was heading for the corner of the net had Fabianski not got across to his near post and turn it behind for a corner. Good shot, even better save.
It's been all Burnley since that Trippier own goal, and they are coming closer and closer to getting off the mark. Swansea have Fabianski to thank should they hold on and leave Lancashire with all three points.
BURNLEY SUB: Any momentum that Burnley had built up over the last 15 minutes or so has seemingly died out completely. Swansea look far more comfortable on the ball now as another striker, Lukas Jutkiewicz, is brought on in place of Barnes for the home side.
SWANSEA CITY SUB: Monk makes his third and final change to completely kill off any Burnley momentum in the closing stages, bringing on Oliveira for Gomis. One minute of added time left to play.
CLOSE! Oliveira pounces on a weak back pass and gets a shot away which trickles right across the face of goal. That looks to be the last attacking move of the game.
Indeed that was the last piece of play of the afternoon as Jonathan Moss brings the game to a close. Kieran Trippier's unfortunate own goal proved to be the difference in the end, a cruel blow for a Burnley side who remain inside the divsion's bottom three following the reverse.
Well that's all from me for the time being, but be sure to stick around as we bring you a full match report, player ratings and analysis from Turf Moor. Thanks for joining!
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