كتب : Hatem Maher
Scottish midfielder Darren Fletcher put the visitors ahead midway through the first half.
He precisely controlled Ryan Giggs' pass inside the area before hitting a low shot into the bottom corner.
United could have extended their advantage before halftime but Everton keeper Tim Howard blocked two decent efforts from Giggs and Cristiano Ronaldo.
But Alex Ferguson's men laid-back approach to the second period allowed Everton to gradually gain control.
The Toffees were rewarded four minutes past the hour mark when Marouane Fellaini rose above Nemanja Vidic to head home Phil Neville's cross.
The result put United in fifth place of the league table with 15 points, five adrift of joint leaders Chelsea and Liverpool.
Watch United's goal
Watch Everton's goal