Arsenal now lead the title race on 47 points, two clear of United on 45. Chelsea sit six points behind the leaders on 41 after a 2-1 home win over Newcastle. Liverpool remain in fourth place on 36 points, but with two games in hand, ahead of their clash at Manchester City on Sunday.
Everton put Arsenal under severe pressure in the early stages of their evening match and it was rewarded with a goal for Tim Cahill in the 20th minute. The Arsenal defence failed to deal with Mikel Arteta's corner and Cahill nodded in from close range.
Just two minutes into the second half however the Gunners equalised after Eduardo latched on to a long ball from Gael Clichy. Eleven minutes later the Croatian put the Gunners ahead with a cool finish past Tim Howard.
Niklas Bendtner was then sent off on his first league start after a dangerous tackle on Andrew Johnson. But just as Everton looked to put the visitors under renewed pressure, they handed the victory to Arsenal as confusion between Joseph Yobo and Tim Howard allowed Emmanuel Adebayor to walk the ball into the net.
Tempers flared again in the final ten minutes of the match as Mikel Arteta was red carded for elbowing Cesc Fabregas in the face. Tomas Rosicky then rubbed further salt into Everton wounds with a thumping strike in the 93rd minute.
Earlier West Ham stunned champions Manchester Utd with a second half comeback after Christiano Ronaldo missed a penalty that would have given United a 2-0 lead.
The champions had led early on through Ronaldo's 13th league goal of the season, the Portuguese player heading in Ryan Giggs' cross in the 14th minute.
But Ronaldo's penalty miss proved to be the crucial moment of the match as West Ham equalised just 12 minutes later.
Anton Ferdinand pulled the home side level with a header in the 78th minute before Matthew Upson gave the Hammers their third straight league win over United when he headed in Mark Noble's free kick just four minutes later.
Manchester Utd assistant manager Carlos Queiroz admitted that his team had been outplayed.
"We didn't expect a result like this but we got what we deserved today," Queiroz said. "The reality is West Ham were the better team today. We were never in control of the game."
West Ham manager Alan Curbishley admitted that Ronaldo's penalty miss was the game's crucial moment.
"Obviously the penalty miss was a big turning point. Not only did it give us a big chance to get back in it, but it galvanised the crowd too," said Curbishley after the match.
Chelsea, in third place, took advantage of United's slip and a controversial decision by the linesman to close the gap on the leaders to six points as they defeated Newcastle 2-1 at Stamford Bridge.
A Wayne Bridge own goal early in the second half had cancelled out the Blues' first half lead from a Michael Essien goal. But just three minutes from the end Salomon Kalou scored the winner for the home side despite appearing to be in an offside position.
Elsewhere, Dimatar Berbatov scored four goals in an extraordinary 6-4 victory for Tottenham over Reading, Sunderland eased out of the relegation zone with a 3-1 win over Bolton while Middlesbrough did eased their troubles with a 1-0 win at Portsmouth.
Wigan slipped to a 2-1 home defeat to Aston Villa, while Birmingham and Fulham finished a goal apiece.