The Red Devils dominated the match in the early stages and were rewarded with an Edinson Cavani opener. They then doubled their lead on the stroke of half-time after Bruno Fernandes struck a wonderful shot into the top left corner.
However, with two goals in quick succession at the beginning of the second half from Abdoulaye Doucouré and James Rodríguez, Everton levelled the scoring.
Scott McTominay then seemed to seal all three points with a wonderful header in the 70th minute, that was until the 95th minute, where Dominic Calvert-Lewin secured a point for The Toffies.
Here are the Manchester United player ratings for the encounter.
David de Gea: 3/10 - An embarrassing performance from the United goalkeeper. He led Everton get back into the game, palming the ball straight into Doucouré's path and then wasn't even close to smothering the Everton striker for their third, even though he was only yards out from the United goal.
Aaron Wan-Bissaka: 5/10 - The right-back was poor in possession for most of the game, but, as usual, made a couple of good slide tackles when Everton were attacking on his flank.
Victor Lindelof: 5/10 - Lindelöf dealt with the threat of Richarlison on the right-flank well, but was suspect in the air for both Everton's second and third goals.
Harry Maguire: 6/10 - This was probably Maguire's worst performance in a while. He wasn't as good as usual in the possession and not great defensively either.
Luke Shaw: 8/10 - The only defender with a good performance, Shaw pressed very well throughout and was brilliant going forward on the left and linked up with his teammates greatly. A brilliant free-kick to assist McTominay for his header.
Scott McTominay: 6.5/10 - The Scotsman looked as if he won the game for United with his header, which was amazingly taken. However, McTominay did not have the best game. He was quite a passenger in the midfield.
Paul Pogba: 6/10 - Pogba had a good start to the match and was pulling the strings in the middle. Unfortunately, he had to come off injured in the 39th minute.
Bruno Fernandes: 8.5/10 - The Portuguese attacking midfielder deserved to be on the winning side. He was linking up play with ease and had a swagger to his style on the night that was encapsulated by his stunning finish for United's second.
Mason Greenwood: 7/10 - A really impressive first-half showing from Greenwood turned into a quiet second-half performance. Overall, the winger was good until he was brought off.
Marcus Rashford: 7/10 - Rashford played a wonderful cross for Edinson Cavani's opener and was good throughout but was unable to convert his own chances when they came to him.
Edinson Cavani: 8.5/10 - He set the tone for United's frontline. Cavani's pressing was incredible and he was good in his link-up. The striker took his header brilliantly and played a great performance.
Fred: 6/10 - After coming on for Pogba in the first half, Fred had an average performance. He brought tenacity in the middle but not much else.
Axel Tuanzebe: 4/10 - He came on to see out the game and was unable to do so, giving away the foul for Everton's free-kick which led to the equaliser.