The defender bundled an effort in from close range to cancel out Nikica Jelavic's opener following James Chester's early red card for the hosts.
James Chester was sent off after just 14 minutes after he was deemed the last man when bringing down Glenn Whelan, but the Tigers were able to keep the visitors at bay before Nikica Jelavic turned home from close range after Tom Huddlestone's shot was parried.
|VIEW FROM KC STADIUM
|By Dan Brett
After James Chester's first-half dismissal, it looked like Stoke would go on to pick up all three points; however, Nikica Jelavic's goal made sure to give his side the best chance of a second successive win.
The Potters huffed and puffed their way through the second half, but it wasn't until the introduction of Charlie Adam that things started to tick for Mark Hughes' men, who went on to bag a late point courtesy of Ryan Shawcross' bundled effort.
Neither manager should be happy with a point, and Hull's fans tried to spur their side into going for a win at the death - but the game finishes at honors even. Overall, Hull was excellent in midfield but Stoke needs more from it forward line.
Steve Bruce will have been delighted with the resolve shown by his gutsy outfit, with the team's Europa League playoff second leg to come Thursday, and a share of the spoils against former colleague Hughes will have ultimately satisfied the home boss.
Hull predictably brought back a raft of players who had not featured in midweek, and the changes looked to have an impact in the early stages with the hosts looking jittery in defense.
The pace and power of Mame Biram Diouf troubled the host and it was made to pay for complacent defending on 14 minutes when Whelan intercepted a poor pass and was brought down by Chester as he ran at goal, Jon Moss brandishing a red card at the defender.
Stoke were unable to make their extra man count, and Hughes opted to replace Whelan with striker Bojan Krkic - who had dropped to the bench.
Before the Spaniard could make any impact on the game, though, Hull went ahead when Begovic could only fumble a long-range Huddlestone strike and Jelavic pounced on the rebound to poke home his shot from an acute angle.
The hosts ended the half looking likely to add to their lead, Stephen Quinn seeing a glimpse of Begovic's goal charged down.
Hull goalkeeper McGregor had to get down well to keep out a Shawcross effort at the start of the second period, but the home team were more than holding their own in terms of possession and field position.
Peter Crouch was sent on to give Stoke more of a physical presence up front and fired one thunderous shot just over, but Diouf wasted a series of chances as Stoke's hopes appeared to be fading.
However, Hughes' men eventually hit back in controversial circumstances as Liam Rosenior's clearance clearly clipped Erik Pieters, though Moss awarded Stoke a throw in.
They eventually flung the ball into the box, with Shawcross prodding home in the scramble, the goal-decision system confirming the ball had crossed the line to spare the visitors' blushes.