An otherwise unremarkable first half in the Potteries came to life in the 31st minute when Norwich midfielder Gary O'Neil was handed a straight red card for clattering into Stoke's Ibrahim Afellay on the touchline.
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It seemed that the Potters had made their numerical advantage count when Jonathan Walters broke the deadlock at the back post four minutes after the restart.
However, the visitors from Norfolk were level within the space of six minutes thanks to Jonny Howson, who sent his half-volley beyond the reach of Stoke goalkeeper Jack Butland and into the back of the net.
The encounter eventually swung in Stoke's favour in the 67th minute, though, courtesy of Spanish frontman Joselu. The summer signing from Hannover had only scored once in a red and white striped shirt before tonight, but he doubled his tally for the club with a driven effort that got the better of Declan Rudd.
The points were then made safe 12 minutes from the end when Norwich centre-back Ryan Bennett headed the ball into his own net.
Stoke have now moved up to seventh position and four points off a Champions League place, while Norwich remain in 15th.