The Reds are held by the league leaders here at Oakwell on a bitterly cold afternoon.
Despite both sides creating a number of decent opportunities, particularly late in the game, it ended goalless in this Sky Bet Championship clash.
Paul Heckingbottom had made two changes to the side that had lost in the FA Cup at Millwall last weekend, with Andy Yiadom returning from injury replacing Jason McCarthy and with Joe Williams suspended following his red card at The Den, in came Stevie Mallan.
It was a very even start to proceedings with nothing created of note until around 10 minutes in when a ball fell to Roman Saiss on the edge of the box but his effort went clean over the crossbar of Adam Davies.
The Reds responded soon after when Adam Hammill found space on Wolves' right, cut in and curled an effort towards goal but it was simple for John Ruddy in the visitors' goal.
It was proving a tough encounter with challenges flying in, no little spirit on show but chances were at a premium. Wolves saw Saiss and Jota booked for poorly timed tackles; Mallan for the Reds was given a yellow card himself just prior to the break.
The closest either side came to breaking the deadlock was probably Ruben Neves' neat curled effort that only just cleared Davies' bar.
The Reds' best openings were from crosses; Ethan Pinnock glanced a header just wide from a Mallan free-kick and right on half time, Brad Potts saw a similar header drift wide after a wonderful Adam Hammill cross.
HALF TIME: Barnsley 0-0 Wolves
Heckingbottom was forced into making a change at the break with the injured Lloyd Isgrove replaced by George Moncur.
On 57 minutes, the away side thought they were ahead when Jota tucked home a cross but he was a yard offside.
Some lovely build-up play by Barnsley, one-touch passing from Potts and Tom Bradshaw allowed room for Mallan centrally, 25 yards out, but he tried bending it into the far corner only for Ruddy to stop with ease.
Wolves then brought on Ivan Cavaleiro in place of Helder Costa, whilst Bradshaw made way for debutant Kieffer Moore up front as Hecky made his second sub.
Leo Bonatini found room inside the box on the angle, but rather than supply his teammates he went for goal but missed awfully. He was replaced immediately by Rafa Mir.
On 74 minutes, a huge chance for Barnsley..
A long throw by Dimitri Cavare was flicked into the six yard box by Pinnock who rose well, the ball dropped invitingly for the on-rushing Hammill but his side-footed effort whistled just wide of the post.
The visitors went straight up the other end and after Mir flicked the ball over the top, Jota hit a terrific half-volley that came crashing back off the bar.
With 10 minutes remaining, Jota somehow fired over from a yard out after some fine wing-play from Cavaleiro on the right.
The final and clearest chance came with five minutes left as Potts fed Moore, he managed to stretch a toe to divert the ball into the path of Moncur who'd made the run into the area, but his shot whilst powerful went wide, much to the frustration of everyone of a Reds persuasion.
FULL TIME: Barnsley 0-0 Wolves
Davies, Cavare, Pinnock, Lindsay, Yiadom, Potts, Mallan (Thiam 87), Gardner, Isgrove (Moncur 46), Bradshaw (Moore 66), Hammill.
Unused: Townsend, Pearson, McCarthy, Brown.