United, needing victory to go second in the Premiership, failed to maintain their exhilarating first-half form beyond the interval.
They petered out badly and Everton could have snatched three points by capitalising on two bad errors by Paul Scholes.
United made too many mistakes throughout.
Goalkeeper Edwin Van der Sar's poor third-minute clearance went straight to James McFadden, he set up James Beattie, who with the goal at his mercy, hit his shot straight at Mikael Silvestre.
More lax defending by the hosts cost them a goal four minutes later.
Kevin Kilbane's mazy run enabled Leon Osman to find McFadden free on the left side of the United box and he beat Van der Sar at his near post with a left-foot shot from the left edge of the six yard box.
United hit back with a glorious equaliser after 15 minutes.
Scholes' magnificent 50-yard pass from just inside the Everton half found Ryan Giggs ghosting into the penalty area and he scored with the deftest of left-foot shots from 12 yards.
United stormed forward looking for a second goal and Everton goalkeeper Richard Wright, who had earlier made a fine point-blank save from Alan Smith, produced another instinctive block to deny Gary Neville.
The second period failed to live up to the first, although United could easily have gifted a goal to the visitors with two dreadful lapses of concentration midway through the half.
Scholes was robbed by Simon Davies and he raced away with McFadden and, as United's defence was stripped bare, Davies set up the Scot to hit a fierce shot from the edge of the box which was brilliantly tipped behind by Van der Sar.
In the 68th minute, Scholes' pass was short of Kieran Richardson short. McFadden again raced away, but this time hit his shot narrowly wide from the edge of the box.