First-half chances were few and far between, but the hosts almost opened the scoring when Ahmed Elmohamady's dipping strike from outside of the area was tipped over the bar by Asmir Begovic.
The best chance of the opening 45 minutes fell to Curtis Davies, only for the Hull defender to glance his header wide following a pin-point delivery from Tom Huddlestone.
An error from Maynor Figueroa could have proved costly for the Tigers, but Marko Arnautovic and Oussama Assaidi were not quite on the same wave-length and it went unpunished.
Stoke did have the ball in the net through Stephen Ireland when he tapped in from close range after Allan McGregor's smart save, but he was denied by the linesman's flag for offside.
The visitors had the better of play as the game progressed, with Ryan Shawcross heading against the crossbar the closest they came before McGregor denied Peter Crouch.
It might not have been a game to rouse the neutrals at home, but a point apiece serves both sides well enough in their attempt to pull away from the relegation scrap.
Stoke boss Mark Hughes rewarded two of the men who helped secure last weekend's shock win over Chelsea, promoting goalscorers Ireland and 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 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 unrest at a corner - but Sagbo was able to clear before the visitors could muster a shot.
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 Davies put an unmarked header wide from Huddlestone's dangerous free-kick.
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 to come and Hull were refused a penalty when Sagbo's header struck Muniesa's arm before Ireland drilled a shot just wide from the edge of the area.
The ball was finally put in the net in the 70th minute but an offside flag denied 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 goal-bound 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.