Gera's 59th minute winner has put Albion within touching distance of a place in the Premier League, but dealt a serious blow to Wolves' hopes of reaching the play-offs.
It also continued a dismal run for Wolves against Albion as Mick McCarthy's side have now lost five of the seven league, FA Cup and play-off meetings between the sides in the last two seasons.
Albion were well worth their success as they twice hit the post through Gera and Kevin Phillips, while Wolves found chances hard to find.
Once they fell behind their best opportunity to salvage a point came from midfielder Seyi Olofinjana, but his 88th minute drive was well held at his near post by Dean Kiely.
Albion should really have taken a lead into half-time, having effectively dominated the opening period in terms of chances.
Ishmael Miller twice went close in the first nine minutes, before Gera slammed a header against the post following a Jonathan Greening free-kick.
Goalkeeper Wayne Hennessey then denied Miller by tipping away his low shot with Phillips failing to stab the ball home on the goalline.
That lucky let-off sparked Wolves into their best spell of the half and the game with Michael Gray being frustrated by a well placed Kiely.
Wolves were then unfortunate not to break the deadlock on the half-hour after a right-wing corner from Matt Jarvis.
Jody Craddock saw his shot blocked and Leon Barnett then headed an effort from Sylvan Ebanks-Blake off the line.
Albion midfielder James Morrison collected the clearance and raced the full length of the field only to see his shot saved by Hennessey.
But Hennessey reserved his best save of the half for the closing moments when he acrobatically tipped a Neil Clement free-kick over the bar.
Clear-cut chances for Wolves were rare and they were made to rue the miss by Gray in the 52nd minute when he failed to convert a Jarvis cross at the far post.
Albion made them pay a heavy price for that and even handed them a warning they failed to heed when Phillips hit the post after 58 minutes following a neat build-up involving Morrison, Robert Koren and Roman Bednar.
Phillips turned provider 60 seconds later after collecting a long clearance by Clement and crossing for Gera to score from just six yards for the game's decisive moment.