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 ever 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, while United remain in fourth.
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 the midfielder picked up possession of the ball, setting Seamus Coleman clear down the right flank, before then collecting his return pass and dancing his way past both Danny Blind and Paddy McNair???s challenges and coolly sliding the ball past the onrushing 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.
In fact, 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 could not hit the target from the edge of the area with just Howard to beat, much to the home fans??? amusement.
However, 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 ended up with Stones powering a header home, despite Ashley Young???s valiant attempts to clear the ball off the line.
As a result, the visitors need to score early in the second period, but like in the opening 45 minutes, much as United huffed and puffed, they rarely tested Everton goalkeeper Howard, with the closet they came to finding the back of the bet coming just after the break.
United centre-back Chris Smalling headed Mata???s right-wing corner into the six-yard box, where a waiting Wayne Rooney failed to beat Everton???s American shot-stopper 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 United???s ineffective forward line, United failed to score for the second league outing in succession.
And the visitors??? 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, only to fail to see the Belgium international lurking right behind him, and the substitute calmly side-footed home to hand the home team their biggest win over United in 23 years.