It was Belgian midfielder Marouane Fellaini who added the only goal of the match with a powerful header just before the hour mark.
Here, Sports Mole dissects the action between the two Premier League rivals.
On target 7
Manchester United statistics:
On target 7
Was the result fair?
On the balance of play, you would have to say yes, just. Everton certainly started the evening the better, with the home crowd calling for every decision. But for the heroics of United stopper David de Gea, United would have entered the break behind. However, the away side did improve in the second period, and perhaps were worthy of a point after dominating the final 30 minutes of the evening.
Ever so compact. Sylvain Distin and Phil Jagielka both had probably the best games they will have in their entire lives, while the midfield worked tirelessly in front of them. Undoubtedly their star player was Fellaini, who was simply sensational. Meanwhile, the likes of Leon Osman and Steven Pienaar ran their socks off.
Manchester United's performance
It is extremely important not to get carried away with United's loss this evening. They had two midfielders playing in defence, while it was Nemanja Vidic's first competitive match since last December. There were also plenty of positives for Sir Alex Ferguson with the performances of Shinji Kagawa and De Gea, but the performances of Patrice Evra are something that need to be addressed.
Sports Mole's man of the match
Marouane Fellaini: The 24-year-old was just unplayable this evening. He emerged into one of the best midfielders in the Premier League last season – and is now THE standout central midfielder for me.
Biggest gaffe of the match
A host of Nani incidents – take your pick. He has all the talent in the world, but time after time he lets you down. Misplaced crosses, passes, they were all there tonight. You just need so much more from him.
Andrew Marriner had a respectable 90 minutes of football. He didn't bow to the crowd's pressure to dismiss those players on yellow cards, although he might have awarded Danny Welbeck a penalty in the opening period.
Everton: Everton face a trip to Aston Villa this weekend when they will be keen to make it back-to-back league wins.
Manchester United: Next up for Manchester United is a home match against Fulham this weekend when they will be keen to get among the goals.