Kortney Hause put the visitors ahead from close range after a flick-on by Dave Edwards, who then headed a second from Connor Ronan's free-kick.
Alex Mowatt was sent off on his debut for Barnsley, with Tykes manager Paul Heckingbottom then sent to the stands.
Edwards smashed in his second, before Marc Roberts scored a late consolation after Adam Hammill's shot was parried.
Barnsley created several chances to level after falling behind, with stand-in goalkeeper Harry Burgoyne making a fine reaction save to deny Mowatt when put clean through by Marley Watkins.
But it soon turned sour for Mowatt, who signed from Leeds United on Friday, when he was shown a straight red card moments before half-time for a sliding challenge on Jack Price.
Paul Lambert made six changes to the starting XI which won at Anfield, but his side could have had a third before half-time had referee Chris Kavanagh not overturned his own penalty decision when Adam Hammill and Bright Enobakhare tussled in the box.
Barnsley's defence, who have conceded more goals than any other team outside the bottom seven, struggled to cope with set-pieces, particularly from Ronan, who also hit the post.
Heckingbottom had to watch most of a ragged second-half from the Oakwell stands after a tussle in the Wolves dug-out.
The defeat, only Barnsley's second in eight league matches, dropped them a place to eighth, while Wolves moved up to 16th.
Barnsley manager Paul Heckingbottom: "It wasn't our night and I am disappointed that we conceded the first two goals like that - and it gave us a mountain to climb. Then came the sending off, so the game was all but over by then.
"The naivety has cost us. That's why we lost. It showed me that we weren't right tonight and we can't keep conceding goals like that."
"I have not seen it again, but on first look it did look like a red card - Alex [Mowatt] has been poor there and let us down. He apologised straight away at half-time. He was up for it, but he's just gone over the edge a little bit."
Wolves manager Paul Lambert: "I thought it was fantastic after coming off the highs of an emotional game on Saturday, possibly the highest emotionally that I can remember.
"The feelings of the players, supporters and staff and everyone was associated with Wolves has been draining after all that had happened at Liverpool, so I decided to change it around, but I thought the three young lads in the team were outstanding.
"This was always going to be a difficult place to come. It was never going to be pretty, it was always going to be direct and the Championship is like that, but I thought we were terrific."
Match ends, Barnsley 1, Wolverhampton Wanderers 3.
Second Half ends, Barnsley 1, Wolverhampton Wanderers 3.
Attempt missed. Adam Hammill (Barnsley) right footed shot from outside the box is just a bit too high from a direct free kick.
Foul by Lee Evans (Wolverhampton Wanderers).
Josh Scowen (Barnsley) wins a free kick in the attacking half.
Andreas Weimann (Wolverhampton Wanderers).
(Barnsley) wins a free kick in the attacking half.
Andreas Weimann (Wolverhampton Wanderers) is shown the yellow card.
Foul by George Saville (Wolverhampton Wanderers).
Adam Armstrong (Barnsley) wins a free kick on the right wing.
Delay over. They are ready to continue.
Delay in match Angus MacDonald (Barnsley) because of an injury.
Substitution, Wolverhampton Wanderers. Lee Evans replaces Bright Enobakhare.
Foul by Bright Enobakhare (Wolverhampton Wanderers).
Josh Scowen (Barnsley) wins a free kick in the defensive half.
Substitution, Wolverhampton Wanderers. George Saville replaces Conor Coady.
Attempt saved. Adam Hammill (Barnsley) left footed shot from the centre of the box is saved in the bottom left corner.
Attempt blocked. Tom Bradshaw (Barnsley) right footed shot from outside the box is blocked. Assisted by Adam Armstrong.
Attempt blocked. Joe Mason (Wolverhampton Wanderers) left footed shot from the centre of the box is blocked. Assisted by Conor Coady.
Goal!  Barnsley 1, Wolverhampton Wanderers 3. Marc Roberts (Barnsley) left footed shot from very close range to the bottom left corner following a set piece situation.
Attempt saved. Adam Hammill (Barnsley) right footed shot from outside the box is saved in the centre of the goal.
Foul by Conor Coady (Wolverhampton Wanderers).
Adam Hammill (Barnsley) wins a free kick in the attacking half.
Jón Dadi Bödvarsson (Wolverhampton Wanderers) wins a free kick in the defensive half.
Foul by Adam Hammill (Barnsley).
Goal!  Barnsley 0, Wolverhampton Wanderers 3. David Edwards (Wolverhampton Wanderers) right footed shot from the centre of the box to the bottom left corner.
Attempt saved. Jón Dadi Bödvarsson (Wolverhampton Wanderers) right footed shot from the right side of the box is saved in the centre of the goal. Assisted by Bright Enobakhare.
Foul by Bright Enobakhare (Wolverhampton Wanderers).
Marc Roberts (Barnsley) wins a free kick in the defensive half.
Substitution, Barnsley. Adam Armstrong replaces Ryan Williams.
Substitution, Barnsley. Tom Bradshaw replaces Marley Watkins.
Attempt blocked. Matt Doherty (Wolverhampton Wanderers) right footed shot from outside the box is blocked.
David Edwards (Wolverhampton Wanderers) wins a free kick in the attacking half.
Foul by Josh Scowen (Barnsley).
Foul by Jón Dadi Bödvarsson (Wolverhampton Wanderers).
Angus MacDonald (Barnsley) wins a free kick in the defensive half.
Substitution, Wolverhampton Wanderers. Andreas Weimann replaces Connor Ronan.
Corner,  Barnsley. Conceded by Kortney Hause.
Attempt blocked. Ryan Williams (Barnsley) left footed shot from the centre of the box is blocked. Assisted by Marley Watkins.
Attempt missed. Gethin Jones (Barnsley) left footed shot from outside the box is close, but misses to the right. Assisted by Callum Evans following a corner.
Wolves maintained the momentum from their FA Cup heroics at Liverpool with an eventful win at 10-man Barnsley.