But the margin of their victory should have been far more decisive as they missed as host of chances - particularly in the first-half - of a game that they dominated.
Barnsley had headed into the game on a high after winning their previous two matches. But they only really came to life in the closing stages as their on-loan Derby County marksman Jon Macken struggled to make much of an impact.
Wolves should have had the game wrapped up by half-time only to be frustrated by their finishing, the woodwork and in-form goalkeeper Heinz Muller.
Collins gave Wolves the perfect start when he headed home a right-wing corner from Michael Kightly but that was as good as it got for Mick McCarthy's goal-shy side.
Barnsley tried to bounce back immediately, but Istvan Ferenczi saw his shot blocked.
It was about all Barnsley could muster in the opening period but they were able to ride their luck to stay in contention.
Stephen Ward should have doubled their lead but shot over in the 19th minute before Freddy Eastwood and Collins both hit the post in the space of a couple of seconds following a Jay Bothroyd corner.
Eastwood's shot on the turn whistled just wide before a last-ditch block by Dennis Souza frustrated Bothroyd.
Muller then came to the rescue of Barnsley in the 37th minute when he did well to push out a close-range shot from Ward after another Bothroyd corner had caused panic in the Tykes defence.
While Wayne Hennessey was a virtual spectator in the Wolves goal, Muller was becoming overworked. Twice in the space of a few seconds in the 56th minute, he denied Collins and Eastwood with smart saves.
Muller then denied Eastwood again eight minutes later as the Barnsley goal led a charmed life.
Hennessey was belatedly called into action in the 67th minute when he comfortably dealt with a rising drive from Jamal Campbell-Ryce.
But that sparked some life into Barnsley and Martin Devaney was just inches away from dragging the Oakwell outfit back on level terms after 76 minutes.
Devaney then saw his 88th minute shot well held by Hennessey before the Welsh international just beat substitute Kayode Odejayi to a weak back pass from Darren Ward as Wolves successfully held on to their narrow advantage.