The Baggies ran out 3-2 winners thanks mainly to a blistering start to the match.
Shane Long drove deep after just five minutes to find James Morrison, who superbly guided his header beyond Rs goalkeeper Julio Cesar.
The hosts doubled their lead when Morrison turned provider, setting up Zoltan Gera, who took advantage of panic in the Rs defence to slot home on 22 minutes.
Adel Taarabt struck the goal of the game on 35 minutes, chesting down and volleying in the same movement to pull one back for the Rs.
But Youssouf Mulumbu extended West Brom's lead on 85 minutes, starting and finishing a move which also involved Jose Reyes.
The Rs gave themselves a chance when Esteban Granero finished superbly to bring the scores to 3-2, but Jose Bosingwa, with the final kick of the game failed to rescue a point with a howler of a miss.
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