It was Raul Jimenez's close-range strike which opened the scoring, the Mexican hitting home from inside the box on 70 minutes, before Diogo Jota added a second six minutes later.
Up until then it had been a game low on chances, with both sides struggling to stamp their authority on the match.
But after taking the lead, Wolves finally found their form to see out victory - regardless of Marcus Rashford's late consolation goal - and reach the last four of the competition.
So how did the two teams fare? See the gallery below for our player ratings.
Player ratings from Wolves vs Manchester United
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