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.
Despite enjoying the majority of possession, Manchester United were handed a shock 3-0 defeat by Everton at Goodison Park on Saturday.
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.
United began on the front foot but were caught out by an incisive Everton breakaway early on.
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.
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