The hosts capitulated in the last 15 minutes to allow their bitter rivals to open up an eight-point gap between themselves and the bottom five teams in the relegation battle
Albion dominated the opening half and took the lead through the Nigerian striker with a deflected strike before Steven Fletcher gave the home side a lifeline.
Both teams had plenty of chances in the second period but strikes from Jonas Olsson and substitute Keith Andrews either side of Odemwingie’s second sealed the points before the striker rounded off the scoring just a few minutes from the end.
Wolves opted for an attacking line-up with Kevin Doyle restored to the starting line-up having scored the winner from the bench against QPR last Saturday.
Fellow striker Sylvan Ebanks-Blake was also included in place of the injured Emmanuel Frimpong and Richard Stearman, who was on the bench.
West Brom also made two changes from their last match with Liam Ridgewell handed a debut in defence in place of Nicky Shorey and Paul Scharner coming into midfield to replace Graeme Dorrans.
The visitors nearly took the lead inside 70 seconds after good work from James Morrison who fortuitously found Jerome Thomas in acres of space, but his shot from six yards was straight at Wayne Hennessey.
Albion dominated the opening 20 minutes, and Hennessey was once again called upon as Odemwingie linked up superbly with Youssouf Mulumbu down the right before shooting straight at the Welsh keeper from an angle when a cut back to Marc-Antoine Fortune could have been the better option.
Shortly afterwards Hennessey once again kept the home team on level terms with a brilliant stop.
Odemwingie this time unselfishly passed the ball into the path of Thomas who laid it back for Scharner ten yards out. On the volley, the Austrian international struck the ball towards goal and a deflection just in front of the keeper forced Hennessey to react superbly to tip the ball over.
But despite Hennessey's heroics, the away side finally got the breakthrough they deserved in the 34th minute through Odemwingie.
After a prolonged period of sustained pressure the home defence was eventually breached as the Nigerian striker cut inside from the right hand side and his shot was deflected off David Edrwards before going through Hennessey’s legs.
Out of absolutely nowhere Wolves rallied, and got themselves back into the game with a superbly worked goal.
Fletcher flicked the ball onto Doyle from a throw in and the Irishman shifted the ball to Ebanks-Blake. The striker then moved the ball to his left where Fletcher swivelled and gave himself a yard of space before rifling a shot into the bottom corner from the edge of the area.
The goal on the stroke of half time seemed to invigorate the home side as they began to dominate proceedings. But, much as the home side had done at the end of the first half to their opponents, Albion managed to score a sucker punch just after the hour mark.
A corner wasn’t dealt with properly and, after something of a goal line scramble, the ball came out to Olsson who volleyed the ball straight at Hennessey who let it through his hands. Jamie O’Hara shaped to clear the ball while standing very close to the keeper but he should have dealt with it regardless.
In a frantic two minutes there could, and perhaps should, have been three more goals, but to no avail.
First Fletcher, who has scored more headed goals in the Premier League than anyone else this season, expertly directed a ball for the top corner from eight yards out before Foster got across to claw it away. From the ensuing corner Roger Johnson got his head to the ball and it appeared destined for the left corner before Mulumbu, on the line, headed it onto the bar.
On the counter attack Odemwingie then mesmerised O’Hara and Ward but, with a free run on goal, he delayed the shot before having his strike cleared off the line by Johnson.
The Nigerian, however, swiftly made amends with a sweeping finish after some poor defending from a set piece. Morrison’s corner found debutant Ridgewell free at the back post to flick to skipper Olsson who inexplicably had more than enough time to control the ball and back-heel to Odemwingie who volleyed the ball home.
As Wolves chased the game they left many gaps in defence and it was breached once more as former Wolves captain Andrews struck via big deflection following good work from Morrison.
Odemwingie then scored his third goal of the match as the home side capitulated. Fortune worked well down the left hand side before his ball found the Nigerian on his own in the area to sweep home and add a further layer of gloss to three vital points for the visitors.