Albion still have work to do to secure Premier League safety after Wolves came from behind to win 2-1 with a goal in the last minute of normal time.
It was an eventful afternoon for skipper Lewis Dunk. He gave Albion a deserved lead with a thumping header as the visitors dominated the first half.
But Dunk was shown a straight red card – his second of the season – for bringing down Fabio Silva with just under an hour played.
Wolves equalised through substitute Adama Traore with 14 minutes to go but Albion seemed to have done enough to secure a point, only for Morgan Gibbs-White to flash a shot into the top right-hand corner in the 90th minute.
To complete a disappointing afternoon, Neal Maupay was shown a red card after the final whistle for using foul and abusive language.
Graham Potter had made one change to the side which beat Leeds, with Alireza Jahanbakhsh coming in for his first Premier League start since December 29 against Arsenal, and only his fourth of the season. Joel Veltman (calf) dropped out.
Rob Sanchez made an excellent early save low to his right to push away Vitinha's shot after Rayan Ait-Nouri broke down the left for Wolves, but Albion were soon into their stride and they went in front on 13 minutes.
A good spell of pressure ended with Jahanbakhsh's right-wing cross being headed out for a corner. Gross took it from the right and Dunk powered a header home for his fifth goal of the season. Albion's captain has now scored more goals (11) since his Premier League debut in 2017 than any other central defender.
Dan Burn had strong penalty appeals turned down after he appeared to be wrestled to the ground by Gibbs-White but the goal had infused Potter’s men with confidence and they threatened again from a 25th-minute set piece.
If anything, Dunk produced an even better header from another Gross corner as he had to generate all the power. His effort was heading for the top corner until Rui Patricio pawed it over. From the next corner Adam Webster got in a more powerful header but it was straight at the goalkeeper.
Neal Maupay was next to threaten, volleying over from Danny Welbeck's ball back to his teammate on the edge of the box as Albion continued to dominate possession while looking secure at the back. They were good value for their lead at the interval.
Wolves were lively at the start of the second half and Sanchez was called upon to keep out a low drive from Morgan-White after he burst across the box, before Dunk’s afternoon took a turn for the worse. Fabio Silva was sent through by Vitinha’s clever pass and Dunk clearly pulled back his shirt, forcing referee Jon Moss to reach for the red card, the skipper’s second of the season.
Potter responded by bringing on Alexis Mac Allister and Jakub Moder for Jahanbakhsh and Leo Trossard. Gross moved to right-back with Moder in front of him and Mac Allister slotted into the left-hand side of midfield.
Albion managed to keep the hosts at arm's length for the next ten minutes, but then Sanchez needed to dive to his right to keep out Joao Moutinho's volley from the edge of the box in the 69th minute as Wolves began to push for an equaliser.
The visitors had held firm but with 13 minutes to go Wolves levelled. Substitute Traore exchanged passes with Silva inside the box and his right-foot shot flew into the top corner with Sanchez having no chance.
Albion had an escape with seven minutes to go when Gibbs-White fired over from ten yards after Traore had won the ball back from Gross and gone round Sanchez to set up the chance. But in the final minute of the 90 Gibbs-White made amends, powering a shot from the left-hand side of the box into the top corner.
Albion: Sanchez, Jahanbakhsh (Moder 60), Webster, Dunk, White, Burn, Bissouma, Gross, Welbeck (Zeqiri 79), Maupay, Trossard (Mac Allister 60).
Subs not used: Steele, Connolly, Alzate, Izquierdo, Tau, Propper.