After beating champion Chelsea and Manchester United in its previous matches, Bournemouth full-back Adam Smith fired the visitors ahead in the 52nd minute at the Hawthorns.
Bournemouth already had a numerical advantage after James McClean was dismissed for a late challenge on Adam Smith in the 34th.
West Brom hit back in the closing stages, with defender Gareth McAuley heading in a 79th-minute equalizer.
But Bournemouth restored its lead eight minutes later when Charlie Daniels smashed home a penalty after Dan Gosling was felled by Darren Fletcher.
Salomon Rondon was then red-carded in stoppage time after clashing with Gosling.
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