The home team were leading 2-0 at the break after strikes by man-of-the-match James McCarthy and John Stones, the young centre-back’s first for his club.
And the game was ended as a contest when Kevin Mirallas took advantage of poor defending from the visitors to make it 3-0 as Everton moved up to 10th in the table.
United remain in fourth, seven points ahead of Liverpool, but having played a game more than the Reds, an anxious end to the campaign could ensue.
Everton made a dream start to the match after taking a fifth-minute lead through McCarthy’s strike – his third for the Toffees – although United will be disappointed to have conceded from their own corner.
Gareth Barry headed Juan Mata’s set-piece clear and then set Seamus Coleman clear down the right flank, before collecting his return pass, dancing through challenges from Daley Blind and Paddy McNair and coolly sliding the ball past David de Gea.
The visitors responded though to the shock of falling behind so early by dominating both territory and possession for the remainder of the opening period, but without ever truly testing Tim Howard in the Everton goal.
United’s best opening before the break fell the way of former Everton midfielder Marouane Fellaini just minutes after going 1-0 down, but the Belgium international could not hit the target from the edge of the area with just Howard to beat, much to the home fans’ amusement.
If Van Gaal thought his men would be going in at the break just 1-0 down, he was mistaken as Everton doubled their lead after 35 minutes following a flurry of right-wing Leighton Baines corners, the third of which saw Stones power a header home, despite Ashley Young’s attempts to clear the ball off the line.
The visitors needed to score early in the second period, but like in the opening 45 minutes, they huffed and puffed without reward, their best chance coming just after the break.
United centre-back Chris Smalling headed Mata’s right-wing corner into the six-yard box but a waiting Wayne Rooney failed to beat Howard from close range.
Despite Van Gaal introducing the likes of Radamel Falcao, British-record signing Angel Di Maria and the returning Robin van Persie in the second period to liven up his ineffective forward line, United failed to score for the second league outing in succession.
And their fate was sealed with 16 minutes to go when Mirallas took advantage of hesitation at the back from Antonio Valencia, who tried to play Romelu Lukaku offside but failed to spot his Belgian colleague. The substitute calmly side-footed home to hand the hosts their biggest win over United in 23 years.
Everton: Howard (7), Baines (8), Stones (8), Jagielka (7), Coleman (8), Barry (7), McCarthy (9), Osman (7), Barkley (8), Lennon (7), Lukaku (7)
Subs: Kone (7), Mirallas (8), Naismith (7)
Manchester United: De Gea (6), Valencia (5), Smalling (6), McNair (6), Shaw (7), Blind (5), Herrera (6), Mata (6), Fellaini (6), Young (6), Rooney (6)
Subs: Di Maria (6), Falcao (6), Van Persie (6)
Man of the match: James McCarthy