West Brom's victory in the Black Country derby will increase the pressure on Wolves boss Mick McCarthy after the home side were demolished.
Odemwingie earned Albion their sixth away success of the campaign and it was no more than they deserved after a woeful performance by the home side
Several unhappy Wolves fans vented their anger towards owner Steve Morgan and chief executive Jez Moxey in the directors box in the closing stages as their side were ripped apart.
Steven Fletcher cancelled out Odemwingie's opener in first half injury-time. But Jonas Olsson restored Albion's lead before further goals from Odemwingie and a Keith Andrews strike made sure of victory.
Albion must be wondering how they failed to wrap up the points during the opening period.
They cut through the Wolves midfield at will with Jerome Thomas and debutant Liam Ridgewell finding acres of space down the left flank.
Only a series of fine saves from Wayne Hennessey kept Wolves in contention.
But ultimately they were second best and one wonders how long much longer Morgan will keep faith with McCarthy after this dreadful performance.
Albion were the first to settle and Hennessey denied winger Jerome Thomas at point blank range after Kevin Foley had been pulled out of position.
The Wales number one dealt with an effort on goal from Baggies debutant Liam Ridgewell and then Thomas dragged a low shot wide.
Paul Scharner just failed to make contact with a low ball across the Wolves box from Marc-Antoine Fortune.
Wolves were being over-run in midfield and Peter Odemwingie's fierce drive was beat out by Hennessey after Steven Reid supplied the telling pass.
Hennessey produced his second top class save of the half to turn over a deflected drive from Scharner after a mistake by Bassong.
Albion were queueing up to have attempts on goal and a Ridgewell effort was blocked.
It came as no surprise when Odemwingie broke the deadlock after 35 minutes.
He was allowed to cut in from the right unopposed and his fierce shot took a deflection off Edwards and deceived Hennessey for his sixth goal of the campaign.
Wolves were at sixes and sevens and seemingly powerless to stop Albion's grip on the game.
But in first half injury-time Fletcher equalised with a typically opportunist finish.
He combined with Ebanks-Blake before beating the dive of Ben Foster with his shot on the turn.
Hodgson made a half-time switch with former Wolves midfielder Andrews replacing Scharner.
Wolves began the second half on the offensive and Gareth McAuley did well to cut out a low Doyle centre with Fletcher waiting to pounce.
The home side were playing at a higher tempo and Fletcher's 20 yard drive was deflected just wide with Foster scrambling across his line.
Odemwingie teed up Thomas 15 yards out but O'Hara's challenge did enough to put him off and he shot high and wide.
The Baggies still looked threatening and Hennessey turned aside a Fortune drive.
But from Morrison's corner, Albion regained the lead through Olsson via an error by Hennessey.
McAuley's initial header clipped the outside of a post and then Johnson hoisted his clearance high into the air inside the penalty box.
Olsson was first to react to the loose ball but Hennessey should have held his shot which slipped from his grasp and over the line.
Johnson came close to equalising when his header was cleared off the line by Mulumbu via the underside of the bar.
Odemwingie could have wrapped up the points when he broke into the West Brom box but his shot was cleared off the line by Foley.
But he was not to be denied and after 77 minutes struck for the second time.
Ridgewell turned a Morrison header back across the box, Olsson back heeled the ball goal-wards and Odemwingie applied the vital touch.
Andrews made it 4-1 with a deflected low drive after 85 minutes and Odemwingie completed his hat-trick from a Morrison cross three minutes later.