Sam Vokes missed a penalty on his Stoke debut as Hull claimed a 2-0 victory at the KCOM Stadium.
Vokes, who signed on a three-and-a-half-year deal from Burnley on transfer deadline day, had an afternoon to forget as his spot-kick in first-half injury time was saved by David Marshall.
Jarrod Bowen had given Hull the lead 60 seconds earlier with a well-directed free-kick.
And though the visitors gamely pressed for an equaliser, they were blunt in the final third and Kamil Grosicki's poked finish in the second half ensured a home win.
That had looked unlikely in the early exchanges of the first half as Stoke were the more threatening side.
And they should have at least tested Marshall after four minutes when Danny Batth launched a speculative punt through the heart of Hull's defence. The ball bounced into the penalty area but James McClean made an unseemly hash of the opportunity.
Stoke defender Tom Edwards might also have expected better from his team-mates when he thundered a low, right-wing cross into the six-yard box. Neither Vokes nor McLean reacted and the ball rattled across the face of goal to safety.
Hull eventually warmed to the task, with factions of the home support believing they had scored after 34 minutes.
But Bowen, unmarked at the far post from Grosicki's corner, could only head into the side-netting when it seemed easier to hit the target.
Suitably inspired, Hull enjoyed a fine spell of pressure which peaked when Bruno Martins Indi fouled Todd Kane just outside the penalty area and towards the right corner of the box.
Bowen looked to have his work cut out from such a challenging angle, but he deftly floated the ball over the wall for his 15th goal of the season.
In a breathless end to the half, Vokes then wasted the chance to equalise after referee Peter Bankes had spotted an infringement on the 29-year-old forward.
Vokes' penalty was not short of power but it was struck too close to Marshall, who saved with his legs.
Marshall was, however, nearly caught out moments after the restart when he misjudged Edwards' cross on the goal line, with the ball hacked to safety from the resulting skirmish.
The Hull goalkeeper then had an even bigger let-off when he needlessly tried to claim Bojan's lofted free-kick. Batth headed towards goal, but the ball struck the top of the crossbar and fell kindly into Marshall's hands.
Stoke continued to probe in numbers, but an over-commitment to the cause played to the strengths of counter-attacking Hull, who impressively doubled their advantage after 64 minutes.
Fraizer Campbell's cut-back found the onrushing Grosicki, whose first-time strike hit the foot of the left-hand post and then the back of the net.
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