Peter Crouch gave Stoke the lead when he beat Joe Hart in the 15th minute, but Javi Garcia scored on his debut for City by heading in a cross from Carlos Tevez to level the match in the 35th.
Garcia then almost scored a last-minute winner but Begovic pushed his header from a corner onto the post and Shawcross chased back after Edin Dzeko lobbed the goalkeeper in injury time.
Stoke brought on former England striker Michael Owen for his debut in the last minute but it was too late for him to make an impression.
Manchester City held to 1-1 draw by Stoke City
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