The hosts started brightly, with Goncalo Guedes volleying over from Matheus Cunha's free-kick and Marshall Munetsi seeing a sharp strike blocked. However, Brighton thought they'd taken the lead through a scuffed Welbeck finish, only for the goal to be controversially ruled out for an offside in the build-up. Not to be denied, the Seagulls were given a golden opportunity to break the deadlock shortly after when Cunha brought Mats Wieffer down in the box, allowing Welbeck to step up to the spot and coolly convert his 10th Premier League goal of the season.
Determined to find a response before the break, Wolves upped the ante in the final third, but Munetsi spurned a couple of half-chances as the visitors maintained their advantage at the break. Having picked up just one victory from their last seven Premier League matches, Brighton knew a positive start to the second period was needed, as Matt O'Riley dragged a long-range effort wide of the target.
That sparked the hosts into life, though, and Cunha nearly found a leveller when his curled strike from 20 yards was expertly tipped around the post by Bart Verbruggen. Pereira made a triple change on the hour mark in the hope of turning the game in Wolves' favour, but the Brighton rearguard continued to hold firm, limiting the hosts to very little in terms of clear-cut chances.
For all of Wolves' pressure, it was the Seagulls who added a second goal with five minutes remaining, with substitute Gruda racing onto Simon Adingra's through ball and lifting a delicate finish over Jose Sa to wrap up a vital victory.