For match photos, scroll to PHOTOSTREAM above left; for stats click on the stats tab. Manager reaction below.
Bryan Oviedo's late goal gave Everton their first win at Manchester United for over 21 years.
Everton boss Roberto Martinez achieved what Manchester United manager David Moyes could not do in his 11 years as manager at Goodison Park as the Merseyside club won at Old Trafford for the first time since 1992, ending United's 12-game unbeaten run.
Wayne Rooney, Patrice Evra and Danny Welbeck were all denied by the woodwork but Everton were impressive and had chances of their own before Costa Rican Oviedo struck four minutes from time.
Victory for Martinez's men stretched their unbeaten run to seven games and left United 12 points behind leaders Arsenal.
Man Utd midfielder Marouane Fellaini returned to face his former club, with Ryan Giggs and Rafael also included for the hosts, but striker Robin van Persie (groin) remained sidelined. Ross Barkley and Kevin Mirallas were restored to Everton's starting line-up at the expense of Leon Osman and on-loan winger Gerard Deulofeu, who impressed in his first Barclays Premier League start against Stoke City on Saturday.
Mirallas almost marked his recall with a goal after only eight minutes, when he cut in from the left and stung David de Gea's palms with a venomous right-foot drive from 20 yards out while former United goalkeeper Tim Howard got down well to deny Rooney at his near post 15 minutes in.
Howard had to be alert once again to thwart Shinji Kagawa and Giggs' header flashed wide of the far post as United got into their stride. The Everton keeper was beaten after 28 minutes but Rooney's deflected shot came back off the post. Romelu Lukaku was a constant menace to the United defence in a frantic first half and De Gea saved the Belgium striker's effort with his feet five minutes before the break.
Moyes replaced Kagawa and Rafael with Nani and Adnan Januzaj only 12 minutes into the second half after Everton came out strong following the interval.
The visitors were bossing the midfield and Oviedo fired narrowly wide of the near post before Rooney was booked for a late challenge on England team-mate Phil Jagielka.
Deulofeu replaced the impressive Barkley after 68 minutes and was presented with a great opportunity to open the scoring within a minute of coming on but De Gea denied the winger after Lukaku had played him in down the right.
United were twice thwarted by the frame of the goal when Evra's header was tipped onto the crossbar by Howard and Danny Welbeck headed the rebound against the bar from eight yards out.
Mirallas' free-kick rattled the post for the visitors but Everton won it late on when Lukaku's cross was tucked home at the back post by the onrushing Oviedo.
Manchester United manager David Moyes: "I'm very disappointed but that's the way it goes. It was tight and we missed chances, but took theirs. We needed a bit of good fortune and we didn't get it. We hit the post a couple of times and Tim Howard made some saves. Everton kept at it and showed what a good team they are.
"We didn't defend the goal well enough so it was our own doing. We had some chances, as did Everton. They have been playing well and that's why they are up near the top of the league. It wasn't about me tonight, I was fortunate to manage Everton and I'm fortunate to be managing Manchester United. It's a big catch up for us now."
Everton manager Roberto Martinez: "I have immense pride, because it wasn't just a game of football. It was a mental block that we had to overcome, because over the years we haven't been able to come to places like this and win. To be able to come here and play with the arrogance we have throughout the game. I'm really pleased and satisfied with the hard work that we put in."
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