Ryan Giggs grabbed the opening goal to extend his record of having scored in every season of the Premier League, and Robin van Persie added a second just before half-time.
Everton fought hard in the second half in an effort to get back into the game but were rarely able to threaten as their own top-four hopes were dented, with United warming up for their UEFA Champions League game at Real Madrid in fine style.
There had been a thought that Sir Alex Ferguson would decide to rest a number of his key players ahead of the trip to the Bernabeu, but the immediate focus was on strengthening their position in the title race after Manchester City's shock loss to Southampton on Saturday and Van Persie was selected alongside Everton old boy Wayne Rooney up front.
It was Everton who were rocked by a late blow before kick-off when John Heitinga stepped in for the unwell Sylvain Distin, and United were quickly into their stride as they looked to take advantage of any defensive vulnerability, although Van Persie squandered a glorious early chance when he fired against the post with his right foot after skipping round Tim Howard.
Van Persie played his part in breaking the deadlock on 13 minutes, though, as he set up Giggs to slot home a precise shot from 12 yards which went in off the post for another landmark goal in an extraordinary career.
Everton responded in typically resilient fashion. Having beaten United at Goodison Park and salvaged a memorable 4-4 draw in the corresponding fixture last term, David Moyes' men showed why they have been beaten just three times this season as they battled back in a bid to get level, with David de Gea forced into a flying save to keep out Leon Osman's long-range strike.
Victor Anichebe was unable to get a shot away from close range after miscontrolling a Kevin Mirallas cross, allowing Rafael to race back and clear the danger, and Everton were made to pay for not capitalising on a good period as United doubled their lead on the stroke of half-time.
Van Persie beat the offside trap to latch onto Rafael's pass as Everton ran the risk of playing with a high line, and he surged through on goal to rectify his earlier mistake by going round Howard and angling the ball into the net, despite the best efforts of a sliding Heitinga.
Marouane Fellaini tormented United in the opening game of the season but was unable to exert his influence here after being marked closely by Phil Jones, although the United man had to be replaced just before the hour mark and Everton also made a change of their own as Nikica Jelavic came on for Anichebe.
Jonny Evans went close to adding a third for United in a goalmouth scramble and Howard produced an acrobatic save to tip Tom Cleverley's powerful volley over the crossbar, while at the other end Everton were frustrated by an organised Red Devils defence.
When Everton did manage to get off shots from distance they were denied by De Gea, who got down well to his left to parry a smart shot from Jelavic, but as the visitors pushed forward there were more gaps for United to exploit and Van Persie dragged an effort wide following a fast break.
United were more concerned about avoiding the late drama that saw them drop points at home to Everton last season, and there were huge cheers at the final whistle as the supporters sensed that the finish line could be in sight with just 12 games to go.