Even with a man extra following Fabio's dismissal for deliberately bringing down Michael Kightly after half an hour, Wolves were able to make little impact at Old Trafford.
Welbeck won the match by finishing off a flowing move midway through the second half, tucking his shot comfortably past Marcus Hahnemann.
All in all, with the contest turning into a keenly-fought affair instead of the sterile stalemate that had gone before, the sending-off was no bad thing, except for Fabio, who cut a dejected figure as he made his way off the field.
Michael Owen had United's best chance before the interval but could only turn a header straight at Marcus Hahnemann, who experienced his own Foster moment just before the break when his attempted clearance was charged down by Welbeck. Fortunately for the veteran American, it bounced to safety.
The goal, when it eventually came, just emphasised the gulf in class. Wolves thought they had the situation under control when Darron Gibson rolled a sideways pass to Michael Carrick 30 yards out.
But within an instant, the England midfielder had created space for Welbeck, whose first time pass was returned in equally promising manner by Owen, who succeeded in providing his young team-mate with an opportunity to run onto the ball, clear of the Wolves defence.
The finish was first-time too. Straight into the bottom corner, as befits a player currently making the graduation from England Under-19 to Under-21 duty and surely destined for even higher honours one day.
Welbeck departed to a standing ovation from United's lowest crowd for four years - which still exceeded 50,000 - for another teenager, Norwegian Joshua King, of whom very big things are expected.