Abdoulaye Doucoure and Lewis Dobbin scored the goals as Everton recorded a 2-0 win over Chelsea at Goodison Park in the Premier League on Sunday afternoon.
Doucoure struck in the 54th minute of the league contest, before Dobbin netted a second late on, with the result moving Everton onto 13 points from their 16 matches this season, keeping them in 17th spot in the table, but they are now four points clear of the relegation zone.
Chelsea, meanwhile, have dropped to 12th due to Fulham's win over West Ham United, with Mauricio Pochettino's side losing for the seventh time in the league this term.
Everton have now won their last three league matches during an excellent run, but it is successive defeats for Chelsea in the Premier League, with the capital outfit unable to respond from their disappointing result and performance against Manchester United on Wednesday night.
The visitors had the first half-chance of the match in the third minute, with Enzo Fernandez striking from the edge of the box, but Everton goalkeeper Jordan Pickford was on hand to make a smart save, before the Chelsea midfielder missed the target from the rebound.
Pickford made another excellent stop in the 14th minute, with England's number one flying across his goal to keep out an effort from Cole Palmer, which looked destined to find the top corner.
Everton's first opportunity came in the 25th minute, with Jack Harrison's expert volley just missing the post.
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Chelsea were forced to substitute their captain Reece James with a fresh injury problem in the 27th minute, and the match drifted for the remainder of the half, with both sides finding it difficult to create in the final third.
Everton made the stronger start to the second period, with Dwight McNeil drawing an excellent save from Chelsea goalkeeper Robert Sanchez.
The home side managed to make the breakthrough in the 54th minute, with Doucoure finding the back of the net after Sanchez had denied Dominic Calvert-Lewin from inside the box.
Chelsea head coach Pochettino introduced both Raheem Sterling and Nicolas Jackson in the 67th minute, with the visitors desperately looking to improve their attacking input.
Sterling was involved for the visitors in the 79th minute, with the Englishman driving into the Everton box, but the home side just about managed to clear their lines, and it was very much a backs-against-the-wall performance from the Toffees heading towards the final 10 minutes.
Dyche's side managed to secure all the points in the 92nd minute, though, with Dobbin firing into the back of the net after Chelsea failed to deal with a corner, with the 20-year-old registering his first senior goal for the club.
Everton will be aiming to continue their impressive form when they head to Burnley on Saturday, while Chelsea's league campaign will continue at home to Sheffield United on the same day.
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