Stoke's Ryan Shawcross had a deflected header clip the outside of the post and Joe Allen missed a glorious chance to level matters before halftime.
Stoke kept knocking on the door in the second half and Erik Pieters headed Phil Bardsley's cross wide with the goal gaping but West Brom hung on to stay eighth in the table, three places above their opponents.
(Reporting by Shravanth Vijayakumar in Bengaluru, editing by Ed Osmond)
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