The Red Devils' defence could not cope with the hosts' threat on the break as, despite enjoying most of the possession, they were taken apart by Roberto Martinez's men
A win would have moved the Red Devils, at least temporarily, into second place but the home side went in front early on when a sizzling counterattack was finished off by James McCarthy.
John Stones capitalised on some slow marking at a corner to head home his first goal for the Toffees shortly before half-time, leaving United reeling, but not even some attacking substitutions could turn things around for Louis van Gaal's men.
A controversial decision to rule Romelu Lukaku as not interfering with play from an offside position saw things go from bad to worse for United as substitute Kevin Mirallas pounced for the third, the visiting defence having failed to play to the whistle.
|VIEW FROM GOODISON PARK
|By Tom Maston
Not even when David Moyes was managing either of these sides did Everton record a heavier win over Manchester United at Goodison Park - and the Toffees fully deserved their best home win over the Red Devils since the 1984-85 season.
For what the hosts lacked in possession, they more than made up for in superb defending and incisive counterattacking play; their resurgence looks to be continuing apace. Louis van Gaal, meanwhile, has plenty to ponder as his team again lacked ideas without Michael Carrick at the base of the midfield and, though they will most likely still qualify for the Champions League, there is some concern that they are not quite the team that most thought they had become after wins against Tottenham and Liverpool.
McCarthy began the move by spreading wide to Seamus Coleman, whose cross was only partially cleared by the recalled Daley Blind. McCarthy then collected the loose ball, skipped beyond weak challenges from Blind and Paddy McNair and calmly slotted low beyond David de Gea.
Marouane Fellaini should have marked his first appearance at Goodison as an opposing player with an immediate equaliser but the Belgian tamely side-footed over the bar with only Tim Howard to beat after nicking possession off Gareth Barry.
Van Gaal's side continued to probe but, for all their territorial dominance, found themselves two down 10 minutes before the break when Stones glanced home his first Everton goal from Leighton Baines's inch-perfect delivery.
The pattern of the first half remained in place despite Van Gaal's introduction of Radamel Falcao and Angel Di Maria, with United continuing to toil in the final third.
And Everton once again punished United on the counter when Mirallas raced onto a Barkley pass that was intended for the offside Lukaku before slotting past De Gea at his near post.
Mirallas was clearly in the mood and forced De Gea into a fine save to keep the score at three with five minutes remaining.
In a rare positive for Van Gaal, Robin van Persie then came on following a two-month injury lay-off but the day belonged to Roberto Martinez and United's place in the top four - which appeared rubber-stamped after their derby win over Manchester City - remains insecure.