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The visiting Merseysiders extended their good run of form at Villa Park, having lost on just one of their last 17 visits.
Fabio Borini, who opened the scoring, found the net for the first time in the Premier League in Liverpool colours since April 2013.
As for Villa, they are without a win in seven Premier League games, six of which they have failed to score in.
Burnley 2-3 Crystal Palace
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Dwight Gayle's late winning goal took his tally for the campaign to 10.
It was a moment that ended Burnley's unbeaten run of three Premier League encounters.
On a slightly brighter note, Danny Ings scored his third goal in his last four outings for the Clarets.
Leicester City 0-1 Stoke City
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Heading into this encounter, the hosting Foxes were unbeaten in their previous four matches in all competitions.
In terms of goals, Leicester frontman Jamie Vardy has failed to find the net in any of his last 17 outings.
Three of Bojan's four goals in a Stoke shirt this season have been scored away from the Britannia Stadium.
Queens Park Rangers 0-2 Manchester United
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Man United midfielder Marouane Fellaini has scored twice in his last three appearances as a substitute.
The away side's other goalscorer - James Wilson - found the net for the first time this season in what was his 12th appearance.
Meanwhile, Harry Redknapp's QPR are without a win in their last five Premier League outings.
Swansea City 0-5 Chelsea
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Diego Costa has scored 18 goals for Chelsea this season, five of which have come in his two appearances against Swansea.
Another summer signing, Cesc Fabregas, became the first player in Premier League history to provide 15 assists in two separate seasons.
Swansea have shipped 11 goals in their last four Premier League games.
Tottenham Hotspur 2-1 Sunderland
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Ten of Tottenham's last 14 Premier League matches have ended in a 2-1 scoreline, with Spurs winning seven of them.
Their winning goal was scored by Christian Eriksen, who found the net for the eighth time in the Premier League this term.
Only David Beckham (15), Gianfranco Zola (12) and Thierry Henry (12) can better Sebastian Larsson's return (11) of goals from direct free kicks.
Newcastle United 1-2 Southampton
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On just his second appearance for the Saints, Eljero Elia found the net on two occasions at St James' Park.
The Saints have scored at least one goal in their last nine Premier League meetings with the Tynesiders.
Newcastle striker Yoan Gouffran ended a Premier League goal drought that had lasted for just over 47 hours.
West Ham United 3-0 Hull City
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Visiting Hull have failed to score in 10 of their last 15 Premier League games.
The Hammers won for the seventh time at Upton Park this season, which is same number as they managed during the whole of the last campaign.
Winger Morgan Amalfitano scored for the third time for West Ham, two of these goals having come as a substitute.
Manchester City 0-2 Arsenal
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Champions City lost for the first time in 12 outings in what was Arsenal's first win at the Etihad Stadium since 2010.
The Citizens have now conceded at least two goals in their last three home Premier League matches. That has not happened since 2002.
Nine of Arsenal's 39 goals this season have been scored as headers - only West Ham (14) have scored more.
Everton 0-0 West Bromwich Albion
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Roberto Martinez's Everton are without a victory from their last six Premier League encounters.
Meanwhile, Toffees centre-forward Romelu Lukaku, who cost £28m in the summer, has not scored in any of his previous eight Premier League outings.
West Brom have kept clean sheets in each of Tony Pulis's three games in charge of the club.
