The Bosnian came up with a handful of saves to deny City, who were desperate for maximum points at the Britannia Stadium, but came up short as Yaya Toure saved the day with a blinding goal.
Prior to the Ivorian's savage strike, Stoke took the lead in the 59th minute when Peter Crouch produced quite possibly the Goal of the Season when he controlled a flick-on with the inside of his right foot before unleashing an unstoppable volley over City keeper Joe Hart's head.
That had the Potteries absolutely rocking and rolling but City, as they did against Chelsea during the week, fought back via a special goal from Toure who let rip from at least 35 yards with his wonder shot taking a slight deflection off Ryan Shawcross and in off Begovic's hands.
That goal allowed City to go equal top of the pile but it will not be the ideal result as title rivals United get set for the Cottagers at Old Trafford with Roberto Mancini left to rue a missed chance with his club in desperate pursuit of the Premiership.
Britannia Stadium, Stoke-on-Trent - 27,353