A much-improved second half display made sure the Baggies secured their first win under manager Sam Allardyce in the Black Country Derby.
Wolves have now failed to win a Premier League game since their 2-1 victory over Chelsea in December; a run of six matches.
The hosts scored twice in five minutes (38 and 43) to cancel West Bromwich Albion’s early lead from the penalty spot.
The visitors pulled parity seven minute after the break through defender Semi Ajayi before Matheus Pereira gave Allardyce men the victory with his second penalty of the match on the 56th minute mark.
"Disappointing, frustrated with the way we played and the result,” said the Portuguese manager after the game.
"The beginning of the second half, we started very poorly.
"Two penalties and a throw-in [were West Brom's goals]. We knew we required better defending. We must rectify it and do better."
“We didn't do a good game or achieve a good result. It means a lot for us and our fans. We didn't do what we should do defensively.
"The start of the second half was very bad. Conceding goals makes our task very hard. We wanted to control the game and be aggressive in defence and we didn't do it.
"We had chances and require better finishing. It's very hard against a team that defends so well with men behind the ball.
"We are all disappointed. We are aware it's not a good moment for us, we have to react to it and work hard.
"We think that a back four is better for us with the players we have, it is time to analyze and see what the next step forwards is."
