It was the highlight of a tricky game for the Red Devils, the 4000th in a row to feature a home-grown player, as they failed to follow up on impressive wins over Tottenham and Manchester City last week.
Harry Maguire and Ole Gunnar Solskjaer both commended the 18-year-old out after his goal on 77 minutes cancelled out a Victor Lindelof own goal in the first half.
"Mason Greenwood is different class in and around the box," Solskjaer told Sky Sports of the striker who has scored twice in his last four appearances.
"You're not surprised when he scores goals. It's fitting that it should be an academy player that scores in the 4000th match, and it makes me hard to leave him out.
"He knows where the goal is and just has the knack. I need to give him more game time.
"We have found just the right moment for him now, he is stepping up.
"We've always had the DNA, with added players from other top clubs, and that will always be the philosophy here."
One of the players that United added last summer, the world's most expensive defender Maguire, was equally effusive about his teen team-mate.
He said the goal was indicative of a more ruthless attitude around Old Trafford.
"He is a goalscorer," the England international said. "He is going to score a lot of goals for this club.
"He is a great player.
"I think you can see the improvements we are making. We looked more clinical today and we are scoring goals now."
Today's match was the first time in five that Solskjaer's men hadn't scored multiple times, scoring 12 in that time.
Greenwood was one of four graduates from the academy at Melwood to feature in the match against the Toffees. He replaced Jesse Lingard, while Marcus Rashford and Scott McTominay played the whole game.
According to Opta Greenwood, who has seven goals in all competitions this year is the third-highest scoring teenager in Europe, behind Jadon Sancho with 11 and Arsenal's Gabriel Martinelli, who has eight.