It might not have been a game to rouse the neutrals, but a point apiece serves both sides well enough in their attempt to pull away from the relegation scrap.
The fixture did not appear to promise a goal glut before kick off, but had it not been for Begovic in the first half and McGregor in he second the stalemate would at least have been broken.
Begovic kept Hull out with good saves from Ahmed Elmohamady and Yannick Sagbo before the break and his opposite number twice prevented Peter Crouch from capping a much-improved Potters display in the last half-hour.
McGregor's first save from Crouch, a one-handed stop from just a couple of yards, landed at the feet of Stephen Ireland but when he tapped home he was flagged offside.
Ryan Shawcross headed against the crossbar as Stoke pushed but Hull held out and now boast the best home defensive record in the division, with just three conceded in eight games.
Stoke manager Mark Hughes rewarded two of the men who helped secure last weekend's shock win over Chelsea, promoting goalscorers Ireland and Oussama Assaidi from the bench to the starting XI.
But there was to be nothing as dramatic from them this time.
Hull warmed to the task quicker than their opponents although their first shot - a 30-yard drive by Maynor Figueroa - was more speculative than anything else.
Their next attempt, after 12 minutes, was much closer to opening the scoring. Danny Graham won a corner with a deflected effort and when Tom Huddlestone's delivery was cleared, Elmohamady took it neatly on his chest.
He struck a sweet volley as the ball dropped but Begovic sprang into action to palm it over the crossbar.
Stoke's response came from a familiar avenue - Crouch's height causing disquiet at a corner - but Sagbo was able to clear before the visitors could muster a shot.
The Ivorian was doing his best work at the other end of the pitch, though, cleverly laying off for Graham only for the on-loan Sunderland man to hesitate and allow Ryan Shawcross to block his belated strike.
After 21 minutes Sagbo went close himself, testing Begovic with a meaty near-post strike after Elmohamady had left Marc Muniesa in his wake. Again the goalkeeper was up to the challenge.
Hull were cranking up the pressure but Stoke survived again when Curtis Davies put an unmarked header wide from Huddlestone's dangerous free-kick.
The centre-half had earlier pleased the crowd by twice showing Ireland a clean pair of heels when carrying the ball from the back.
The Potters, spurred on by some impassioned prompting from Hughes in the technical area, tightened up to reach half-time without allowing Hull's pressure to tell.
Stoke came out after the break with a little more endeavour than before and might even have nicked the lead had Shawcross managed a clean connection to Marko Arnautovic's flat corner.
On the hour, Begovic again kept Stoke in it.
Sagbo and Graham made inroads into the Stoke area before Figueroa's cross found Elmohamady at the far post. His header lacked real power but still required a smart save from the Bosnian keeper.
From that point on, it was Stoke who took the game by the scruff of the neck.
Figueroa almost gifted the advantage when a dreadful touch left Stoke with a two-on-one advantage and acres of space. Arnautovic was the man in possession but, with Assaidi crying out for the pass, he wrongly went it alone and was dispossessed.
The chances continued as Hull were refused a penalty when Sagbo's header struck Muniesa's arm and Ireland drilled a shot just wide from the edge of the area at the other end.
The ball was finally put in the net in the 70th minute but an offside flag was against Stoke.
Geoff Cameron's superb cross found Crouch at the far post and had his header not been brilliantly clawed back by McGregor it would surely have been 1-0.
But Ireland, a fraction ahead of James Chester, became active as soon as the save was made and his point-blank finish was chalked off.
McGregor produced another fine save moments later, tipping Crouch's goalbound attempt wide, and the resulting corner was headed against the bar by Shawcross.
As Stoke pressed, the hosts looked more ragged but held on to share the spoils.