Marouane Fellaini was the best player on the pitch and topped that performance off with a 57th minute header from a Darron Gibson corner to allow Everton to become the first team in eight years to beat United on the opening weekend of the season.
David Moyes' men were the better side on the night, providing plenty in attack in the first half, before defending strongly when Sir Alex Ferguson's charges tried in vain for a leveller.
All the talk prior was about the Red Devils' new signing Robin van Persie, who joined from Arsenal for £24million, but he started on the bench and only came on with just over 20 minutes remaining. He had little impact on the match, sending in a few corners, but was close to combining with fellow new boy Shinji Kagawa in the 79th minute only to see Toffees keeper Tim Howard equal to the task.
Of the glovemen, United's David De Gea was by far the busiest, making a number of quality saves to deny Fellaini from a tight angle in the 14th minute and the coming up with a low block to keep out Steven Pienaar prior to his reaction stop when Leon Osman fired on the turn from close range.
Everton had a great chance to go ahead early in the second term when Osman's volley rattled the underside of the crossbar but thankfully Fellaini, who won everything in the air, was able to fire home his header from the edge of the six-yard box prior to the hour-mark.
United threw everything forward in the final 20 or so minutes but the defensive effort of Everton, led by the back four of Leighton Baines, Tony Hibbert, Phil Jagielka and Sylvain Distin, was brilliant as the perennial slow starters recorded maximum points in somewhat of a surprise result early in the season.
Goodison Park, Liverpool - 38,415