Watch: Wolves shock Man United to reach FA Cup semis
United lacked spark throughout and were overcome by an eager Wolves side with two goals in the space of six minutes in the second half from Raul Jimenez and Diogo Jota.
Marcus Rashford's injury-time effort was a mere consolation.
United were favourites but the Midlanders' form against the top six that has carried them to seventh position in the Premier League gave home fans hope.
The early signs were that United, not Wolves, were going to live up to the hype of the warm-up, dominating early possession.
Wolves' first threat came in the 28th minute when Ruben Neves's low drive was well held by the United goalkeeper Sergio Romero and it was swiftly followed by a better one, Jota failing to connect properly with a volley from Matt Doherty's centre.
Nuno Espirito Santo's side were gaining in confidence however and created two chances that required some superb goalkeeping from Romero.
First he reacted sharply to tip over a bullet header from Jimenez from Joao Moutinho's corner.
The Argentine keeper then palmed over...