The Carling Cup holders, fielding a totally different eleven from the side which started Sunday's Manchester derby scored their winner after 66 minutes.
Welbeck played the ball to Michael Owen just outside the Wolves box and the England striker returned the perfectly weighted pass for the 18-year-old forward to score with a crisp low right foot shot from 12 yards.
United had been reduced to ten men just before the half-hour mark when left-back Da Silva Fabio was sent off.
Wolves striker Stefan Maierhofer won an aerial dual with Jonny Evans in the centre circle. The ball bounced clear and, although Wes Brown won his tackle with the marauding Maierhofer, it rebounded into the path of Michael Kightly.
Kightly raced clear and, with only Fabio standing between goalkeeper Tomasz Kuszczak and the United goal, the Brazilian wrestled Kightly to the ground, leaving referee Peter Walton with no alternative but to order him off.
In a game of few chances, the best fell to the visitors. The closest they came to scoring was from the free-kick awarded after Fabio's dismissal.
The ball was teed up for former United player David Jones who hit a sweet 20-yard shot from the edge of the box which produced an excellent one-handed save from Kuszczak.
The bulk of Wolves' chances fell to Kevin Doyle who replaced another former United player, Sylvan Ebanks-Blake, in the 65th minute.
Doyle had four good chances - the best coming when he raced down the right before cutting across the edge of United's penalty area and firing in a shot which was well saved by Kuszczak at full stretch.
In contrast, United's chances were less clear-cut. They hit the post shortly before their goal when Nani's right-wing cross came off Wolves left-back George Elokobi and onto the upright with Wellbeck waiting to strike.
A minute into stoppage time, United's best player, Darron Gibson, hit a fizzing 25-yard drive which Wolves goalkeeper Marcus Hahnemann took under his bar.