The game marked Ole Gunnar Solskjaer's100th match as manager of United in the Premier League. A record which sees him with 53 wins, 19 losses and 28 draws in charge.
The win is also United's 28th unbeaten away from home which is a Premier League record.
Greenwood had a golden opportunity to put United ahead on 45 minutes after being put through into the box by Bruno Fernandes but he failed to make the most of the opportunity.
Adama Traore caused Solskjaer's side trouble in the first half but the lack of finesse in his finishing saw the result stay level at the break.
The second half started much the same as the first with United continually frustrated.
A double save from David de Gea on 69 minutes made sure the home side didn't break United's unbeaten streak on the road.
Joao Moutinho drifted a corner into the box which Romain Saiss headed towards De Gea who punched away. However, the ball broke to Saiss again and the United goalkeeper was forced into another impressive save.
"It was so quick, the first one hit my body and then I made the double-save. It was good because the team, after the save, scored the goal, we won a massive three points," De Gea said after the match.
It was United, though, who finally broke the deadlock on 80 minutes through Greenwood. Paul Pogba pulled the ball wide to Greenwood who hit it low and into the net.
Wolves were adamant there was a foul on Ruben Neves in the build-up to the goal but nothing was given.
"Everyone saw it, everyone saw my leg, we always do meetings and everything with referees about VAR, I don't know why," he said.
"They said before the season started they will look for contact -- if the contact is strong enough, they will give the foul. I showed them my leg.
"I think maybe because last game it was a foul before the Southampton goal, maybe now they did the opposite. I showed my leg to the ref, I showed to the assistant ref, I cannot say anything more."