The Everton manager has had to defend himself during a testing second season on Merseyside, but the Spaniard got his tactics spot on to earn a morale-boosting win on Sunday courtesy of goals from James McCarthy, John Stones and Kevin Mirallas.
Heeding the blueprint of Chelsea’s victory over United last week, Everton sat deep throughout, allowing the visitors to dominate possession before breaking quickly with Aaron Lennon, Ross Barkley and Romelu Lukaku.
Everton’s fifth-minute opener came via a swift counter, with McCarthy applying a superb finishing touch to a move that he started.
The hosts’ second goal also arrived after a spell of United pressure, with Stones’ near-post header from Leighton Baines’ corner giving Everton a two-goal cushion 35 minutes in.
Van Gaal introduced Radamel Falcao for Marouane Fellaini, who missed United’s best chance of the match, at the break in an attempt to sharpen his side’s cutting edge. But it made no difference. Everton substitute, Mirallas, completed the scoring 16 minutes from time to condemn United to a second straight defeat, their first since December 2013, and their heaviest in the Barclays Premier League under Van Gaal.
United began on the front foot but were caught out by an incisive Everton breakaway after four minutes. McCarthy began the move by spreading wide to Seamus Coleman, whose cross was only partially cleared by the recalled Daley Blind. McCarthy collected the loose ball, skipped beyond challenges from Blind and Paddy McNair and slotted low beyond David de Gea.
Fellaini could have marked his first appearance at Goodison as an opposing player with an immediate equaliser, but the Belgian side-footed over 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 2-0 down 10 minutes before the break when Stones glanced home his first Everton goal from Baines’ delivery.
The pattern of the first half remained in place after the break despite Van Gaal’s introduction of Falcao and Angel di Maria, with United continuing to toil in the final third.
Everton again punished United on the counter when Mirallas raced on to a Barkley pass that was intended for the offside Lukaku before slotting past De Gea at his near post.
Mirallas 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 came on following a two-month injury layoff, albeit for a hobbling Wayne Rooney, but the day belonged to Martinez.
United’s place in the top four, which appeared certain after their derby win over Manchester City, has yet to be guaranteed. They are on 65 points, seven clear of Liverpool, a place below in fifth, having played a match more.
Everton, meanwhile, moved above West Ham United into the top half of the table with 44 points.