West Brom could have moved into fourth place in the Premier League with victory but their hopes fizzled out in the rain as Pablo Ibanez and Gonzalo Jara were sent off before half-time.
Ibanez was unfortunate when his momentum took him into D.J. Campbell after the striker turned sharply in the penalty area after 12 minutes. Charlie Adam slotted home the resulting spot-kick.
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There was no doubt about Jara's red card when the Chilean inexplicably launched into a crazy tackle on Luke Varney near the corner flag.
West Brom looked capable of an equaliser despite their numerical disadvantage but Varney doubled Blackpool's lead after 62 minutes when he slid in to meet Elliot Grandin's low cross.
What should have been an enjoyable final few minutes for the home crowd became fraught with tension when Youssouf Mulumbu weaved into the area and finished in style.
In a breathtaking finish to the game, Graham Dorrans wasted a great chance to snatch an unlikely point for the visitors when he blazed a last-minute chance over.
Blackpool moved up seven places to ninth and West Brom, like their opponents promoted to the top flight this season, remained sixth after their first defeat since losing to Liverpool in August.
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