The result comes as Sam Allardyce’s first win as Baggies boss and brings them to within touching distance of moving out of the drop zone.
And it was the under pressure visitors who were the brighter side in the opening stages with Wolves gifting them an opener on eight minutes.
Willy Boly collided with Callum Robinson inside the box and star man Matheus Pereira calmly tucked home from the spot.
But that goal only served wake Wolves up as Adama Traore tested David Button and Portuguese international Pedro Neto lashed wide.
And with the traffic heading in one direction Wolves netted a quick-fire double to take the lead before the break.
Fabio Silva turned home his first Molineux goal before Boly made up for his penalty gaffe as he reacted quickest to smash home from a corner.
But despite ended the first period strongly the game was flipped on its head once again within minutes of the restart.
Centre back Semi Ajayi bulleted a header past Rui Patricio and Robinson tumbled inside the box once again and Pereira fired home.
The tie did rock back in Wolves’ favour in the closing minutes and Nelson Semedo missed perfect chance to nick a point.
Full Time on a cracker of an afternoon at Molineux it’s Wolves 2 West Brom 3