The struggling hosts had looked like the only winners from the moment Ben Burgess gave them a 34th minute lead.
A controversial 81st minute penalty, given against the otherwise excellent Stephen Crainey for a challenge on Carl Hoefkens, gave the Baggies the lift they needed to turn the game around.
Veteran hitman Kevin Phillips, who had struggled to make an impact after coming on with 25 minutes to go, stepped up confidently to hit the inside of the post and level the scores.
Two minutes later Ishmael Miller found space on halfway and showed off his athletic prowess to fight his way to the byline, before pulling a cross to the near post where Phillips gave it the slightest of touches to send the 1,600 travelling fans into raptures.
Blackpool could barely believe the turnaround in fortunes and threw on loan striker Grant Holt and midfielder Keith Southern in a desperate bid for an equaliser.
But Miller was able to exploit the gaps in the home defence to complete the scoring on 84 minutes.
Blackpool, benefiting from a weekend off, enjoyed the better chances from the start with Crainey particularly influential with his deadly left-footed set pieces.
It was a Crainey free-kick which almost broke the deadlock on just 12 minutes with Burgess rising highest at the far post but heading against the bar.
The same combination paid off to create the first goal, with Burgess getting ahead of his marker to plant a firm header past Dean Kiely.
Blackpool could and should have added to their lead either side of half-time with Stephen McPhee and Gary Taylor-Fletcher both going close.
But ultimately it was the expertise of Phillips and Miller which took Albion back to the top of the table at the business end of the season.