Odemwingie, making his first start of the season, pounced on a mistake by Norwich defender Ritchie de Laet in the third minute to clip a neat finish into the bottom corner.
The former Lille and Lokomotiv Moscow forward had a penalty saved in the 76th minute following Steve Morison’s clumsy challenge on Steven Reid but that miss didn’t affect the result, leaving Norwich without a win after four games back in the top division.
West Brom had lost its first three games of the season, including defeats to expected title contenders Manchester United and Chelsea.
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