The only goal of the game arrived four minutes from time courtesy of full-back Bryan Oviedo, who stole in at the back post to score.
Below, Sports Mole looks back over the contest to determine if the Toffees were deserving of the spoils.
On target 6
On target 4
Was the result fair?
There were times when the Everton goal lived a charmed life, but on the flip side, United should also be criticised for their poor finishing. The visitors were positive from the word go and were rewarded with a late winner. A draw would probably have been the fairest outcome, but Roberto Martinez's side should not be begrudged their victory.
Man United's performance
Frustrating - if ever a display summed up United's season to date, this was it. They created chances and hit the woodwork twice, but once again they were overrun in midfield and looked lapse in defence every time Everton went forward. It won't have told David Moyes anything that he doesn't already know - he needs midfield and defensive reinforcements.
When Moyes took Everton to Old Trafford, some supporters bemoaned their lack of ambition under the Scot. He often set the Merseysiders up not to concede, which they usually did! Here, Martinez sent out his charges with a real positive intent, with Ross Barkley in particular shining before he was substituted. Yes they rode their luck on a handful of occasions, but they also caused problems themselves.
Sports Mole's man of the match
Gareth Barry: As a Manchester City player on loan at Everton, Barry will have really enjoyed this result. He was by no means in the thick of the action for the entire 90 minutes, but what he did was calm Everton down when United started to apply pressure. His passing was precise and he rarely wasted the ball. Such experience proved crucial for the Toffees.
If there is one criticism hanging over Danny Welbeck, it's that he doesn't score goals. He had the perfect chance in the closing stages, but with the goal gaping and Tim Howard stranded, he sent a headed effort against the crossbar. It looked easier to score for the England international.
It wasn't Martin Atkinson's best outing, it must be said. He failed to spot numerous fouls, for both teams. There was also a couple of occasions where he enforced the advantage rule when there was none to be played.
Man United: The Red Devils will remain at Old Trafford on Saturday when Newcastle United make the trip to Manchester.
Everton: It's another away fixture for Everton next time out when they travel to the capital to take on Arsenal at the Emirates Stadium.