In a game of few clear-cut chances, the Seagulls had arguably the best of them midway through the second half when Solly March fired over after being picked out in space inside the box.
In the closing stages Alexis Mac Allister came off the bench for his debut and the Argentina midfielder showed real quality with two free-kick deliveries, the first of which had to be headed clear by Matt Doherty while a shot from outside the box tested Rui Patricio.
At the other end skipper Lewis Dunk made one outstanding block tackle when substitute Daniel Podence seemed to set to score.
It was by no means a classic, but Albion thoroughly deserved something for their efforts. They were well organised, worked hard and looked a threat on the break.
Graham Potter named an unchanged side but there were two changes on the bench with Shane Duffy and Mac Allister coming in, the Argentinian for his first taste in the matchday squad.
The first half took a long time to ignite, not that Albion were complaining as they kept an expectant home crowd quiet.
Wolves began brightly without mounting a serious threat on Maty Ryan’s goal in the first 15 minutes and the visitors gradually began to work their way into the game.
A good move on 18 minutes led to the only shot on target in the first half when Davy Propper, who scored when the sides shared four goals at the Amex in December, fired straight at Patricio from the edge of the box.
Wolves’ best moments in the first half were created by Diogo Jota on the left. In the 37th minute he picked out Ruben Neves in space on the edge of the box but his shot flew well over. Raul Jiminez then nearly profited when Adam Webster misjudged the flight of a long ball but he was offside as his spectacular volley from an angle clattered off the stanchion.
Martin Montoya and Wolves’ Romain Saiss were booked and at the break Potter would have been pleased. Albion had enjoyed more possession and restricted the hosts to few clear-cut opportunities.
Albion made a good start to the second half and Neal Maupay was inches away from touching in Leandro Trossard’s left-wing cross after the Belgian linked up well with Aaron Mooy.
Dunk and Dan Burn were both booked for fouls on Jota and Raul Jiminez respectively as Wolves’ fans began to find their voice and Webster did well to block Neves’s pile-driver from the edge of the box as the hosts began to up the tempo.
Albion had their best chance so far in the 66th minute. After some patient approach play Trossard picked out March 15 yards out and he shot over when he had space to take a touch and test Patricio.
Dunk produced a fantastic block in the 76th minute to frustrate substitute Podence, who seemed certain to score after Adama Traore, who had also come on, picked him out 10 yards from goal. The ball broke to Jiminez, but his effort was straight at Ryan.
With ten minutes to go Mac Allister replaced March then Alireza Jahanbakhsh came on for Trossard. The Argentinian midfielder was involved straight away, whipping in a free kick which Matt Doherty headed away from inside his six-yard box before letting fly from the edge of the box with a shot which was blocked by Leander Dendoncker.
Another Mac Allister free kick in stoppage time just needed a touch and Albion would have been claiming three points. Instead it’s another point on the board which keeps them 15th in the table after none of the sides below them picked up any points.
Albion line-up: Ryan, Montoya, Webster, Dunk, Burn; Bissouma, Propper; March (Mac Allister 80), Mooy (Stephens 88), Trossard (Jahanbakhsh 82); Maupay.
Unused subs: Button, Duffy, Gross, Murray.
Attendance: 31,490