After the tie ended goalless after 90 minutes, the under-21 clash went straight to penalties and it was the Red Devils who emerged victorious, converting four of their spot-kicks to Wolves’ one.
Joe Hodge was the only Wolves penalty-taker to find the net.
The home side had chances to progress and were the better side in the first 45 minutes with Nathan Fraser seeing a shot tipped on to the post in the early stages.
Fraser forced another fine save from the United keeper while Dylan Scicluna and Chem Campbell also had chances to break the deadlock.
Campbell went close in the second half from the edge of the penalty area before Fraser found the net with a header, only to be flagged offside in the dying minutes as the clash ended goalless.