First-half goals from the Welshman and the Dutchman were enough for the Red Devils to extend their lead at the top of the table with a comfortable win at Old Trafford
Ryan Giggs' early goal was followed by Robin van Persie's 19th league strike of the season as United collected a routine three points at Old Trafford.
With a tricky Champions League trip to Real Madrid looming in midweek, Sir Alex Ferguson made three changes as Nemanja Vidic, Phil Jones and Giggs all came into the team.
Everton, meanwhile, brought Phil Neville back but also required a late defensive change after Sylvain Distin dropped out in the warm-up and was replaced by Johnny Heitinga.
The hosts began the game strongly and might have taken the lead as early as the 10th minute. Rafael and Wayne Rooney combined to free Van Persie, who rounded goalkeeper Tim Howard but could only hit the post with the goal gaping.
Minutes later, however, Giggs made no mistake, opening the scoring and continuing his outstanding record of scoring in every Premier League season.
Antonio Valencia's pass was headed down by Van Persie into the Welshman’s path and he calmly took a touch before slotting it past Howard and in off the post.
Yet Everton came right back into the game and could have equalised on the half-hour mark. A great piece of play saw Steven Pienaar find Leon Osman and his fierce strike was creeping into the corner before a flying David de Gea pushed it around the post.
From the resulting corner United required another superb piece of defending to preserve their lead as Vidic bravely threw himself in front of Kevin Mirallas' shot when the Belgian looked set to fire home an equaliser.
Mirallas then almost set up Victor Anichebe. His cross from the right, however, was just behind the striker, who had got in front of Jonny Evans, allowing Rafael to hack it out of play for a corner.
The visitors were made to rue those misses too as United doubled their lead right at the end of the half. Again Rafael was involved, dinking the ball through to Van Persie, who beat the offside trap, rounded Howard again and this time made no mistake, despite the valiant attempts of Heitinga on the line.
The second half was a more subdued affair, with chances few and far between, and United having the better of the opportunities.
A Van Persie corner from the right was met by Evans, whose effort was saved by Howard, before the ball came back out to the defender causing an almighty goalmouth scramble which somehow the Toffees managed to clear for another corner.
The ball in was again not dealt with fully by the visitors and headed out only as far as Cleverley, who smashed a superb volley goalwards only to be denied by a magnificent save by Howard.
As time ticked away Van Persie dragged a shot wide after being set up by Giggs, before De Gea saved well from Jelavic but there was to be no late show from the Toffees this time as United stood firm to take all three points.