French midfielder Giannelli Imbula fired Stoke ahead after nine minutes with a rasping 25-metre volley, his first goal for the club since his big-money arrival on transfer deadline day.
Ibrahim Afellay doubled the lead with a neat finish from a cross by Jonathan Walters and substitute Joselu headed in moments after coming on to confirm Stoke's first win in five league games.
Matt Ritchie scored a consolation for Bournemouth with a crisp strike.
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(Reporting by Ed Osmond; editing by Martyn Herman)
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