The day started perfectly for United when a fantastic long range strike from Antonio Valencia sent them on there way but the visitors really frustrated United after that until the late flurry of goals.
Both managers made interesting team and tactical changes to their teams for the game
Both managers tweaked their side's from their last Premier League games with José Mourinho making three changes to his side from the draw at Stoke City with Marouane Fellaini, Ashley Young and Juan Mata coming into the side to replace Paul Pogba, Matteo Darmian and Ander Herrera.
On the other hand, Koeman went back to what worked for them away at Manchester City earlier in the season by playing a 5-3-2 formation but what they lacked was confidence coming into the game on the back of three defeats.
Valencia's stunner gave United the perfect start
The confidence that the visitors lacked at the start of the game wouldn't have been helped when they went behind in the fourth minute. Valencia, who doesn't score many, hit a piledriver of a half volley into the top corner of the net passed Jordan Pickford, who had no chance of saving it, after Nemanja Matic crossed the ball to the United right back.
Therefore, it was expected that the hosts would pile more pressure on the visitors after the early goal but they didn't and that allowed the visitors to start gaining confidence and they almost punished United on the break.
Lukaku missed two big chances in the first half to net against his old side
The visitors continued to have joy but they were almost caught themselves on the break when a stray ball from Michael Keane found Mata, who in turn played the ball to Lukaku but after the striker had done all the hard work he put the ball wide when he should have scored.
Lukaku was denied again later in the half when a pass from Marcus Rashford released the striker but a last ditch tackle from Phil Jagielka stopped the striker from netting against his old team.
Therefore, after such a poor start to the game, Koeman's men got themselves to the break only a goal down which they would have felt they could pull back in the second half but they also had to be wary of the threat that United possessed on the break.
Two big saves from De Gea kept United in front at the start of the second half
In terms of the second half, the visitors made the better start and they really should have got an equaliser a minute after the restart when Rooney got himself into space in the box but he hit his shot straight at De Gea when he really should have scored.
Koeman's men continued on from there and De Gea was forced into making another great save this time from Gyfli Sigurdsson, who again found himself in space inside the United box.
United really needed to wake up after these chances and they did as Mata came very close to getting a second goal for United. Mata took a free-kick from the edge of the box and was unlucky to see his shot come back off the post with Pickford beaten.
Three late goals sealed another important three points for United
The second goal did finally come for United though when a mistake from Ashley Williams presented the ball to Lukaku, who played the ball through to Mkhitaryan, who in turn calmly slotted the ball into the back of the net.
The second goal really did kill the game but it didn't stop United from going forward and Lukaku did finally get a goal against his old club. After taking the initial free-kick, Lukaku was presented with an easy chance to score when Jesse Lingard flicked the ball into his path from Matic cross and he let his old fans know about.
Just to rub insult to injury, Mourinho's men added a fourth goal in injury time. The goal came from the penalty spot after Morgan Schneiderlin handled the ball in the box as Martial went passed him.
Martial himself stepped up to take the penalty and he calmly sent Pickford the wrong way to seal the win for United but the scoreline at the end of the day was very harsh on Everton, who showed some character in the game.