David Vaughan had put Blackpool in front in Saturday's Premier League encounter but Albion replied through Odemwingie and James Morrison only for Gary Taylor-Fletcher to level for the Seasiders.
But then Odemwingie struck with three minutes remaining to move Albion away from the relegation zone.
Blackpool, fresh from their mid-week triumph over Liverpool, played with their customary freedom with the in-demand Charlie Adam in fine form in midfield.
But they were left to rue two missed chances by the normally deadly DJ Campbell.
The Baggies were unsurprisingly devoid of confidence in the first half after their recent poor run.
But they were dragged up off the floor by the driving force in midfield of Youssouf Mulumbu.
Jerome Thomas also posed problems with his pace and crossing power from the left flank.
Campbell missed a golden chance to put his side ahead after only two minutes.
Luke Varney's pass picked out the Seasiders top scorer and he evaded the challenge of Paul Scharner to leave himself with only Boaz Myhill to beat 10 yards out.
But Campbell contrived to screw his shot wide of the post when it looked easier to score.
The Baggies tried to retaliate and Odemwingie's cross from the left of the box found its way to acting skipper Chris Brunt at the far post.
But he opted to volley rather than head towards goal and was high and wide with his attempt.
Blackpool went ahead after 11 minutes through a superb goal from Vaughan.
Stephen Crainey's cross was only half cleared to Vaughan 20 yards out. The midfielder had time to line up his shot - with no Albion player closing him down - before curling it past the dive of Myhill for his second goal of the campaign.
Albion tried to build up some momentum with Thomas posing the main threat and Brunt seemed certain to convert his deep cross but Crainey made a superb block.
Crainey was then relieved when he made contract with a cross from Thomas under pressure from Odemwingie and forced Richard Kingson to save away to his right.
Then after 37 minutes Odemwingie brought the Baggies back on level terms.
Graham Dorrans supplied the telling ball from the left.
Odemwingie beat the offside trap, controlled the ball and slipped it past Kingson for his seventh goal of the campaign.
Odemwingie then went for goal after being freed by Thomas but he shot wide when Brunt was better placed in the centre.
A second glaring miss of the game from Campbell prevented Blackpool from regaining the lead early in the second half.
Adam's perfectly timed pass enabled Campbell to beat the offside trap but he slipped the ball past the post from 10 yards out.
It proved a costly miss as Morrison put Albion in front after 52 minutes.
Kingson got his hand to a low ball across the box from Thomas but Morrison was on hand to make no mistake at the far post.
Vaughan became the first player to be yellow carded for a challenge on Mulumbu.
Odemwingie found himself one on one with Kingson who spread himself and smothered the shot.
Albion squandered another great chance when Odemwingie teed up Morrison who shot over from 10 yards out.
With 10 minutes left, Taylor-Fletcher levelled for Blackpool when he turned home Phillips' low cross.
Back came Albion and Kingson blocked an effort from Simon Cox.
But in the 87th minute Odemwingie held off Cathcart after a long ball forward and drilled his shot wide of Kingson for the winner.