Paul Gallagher stabbed home Kevin Harper's cross after 74 minutes to give Stoke a win that they barely deserved after Hull had controlled the game for long spells.
After the match Hull manager Peter Taylor hit out at the performance of referee Colin Webster, who denied Hull a first-half penalty when Nick Barmby appeared to be brought down by Marlon Broomes.
"I don't think we are getting the rub of the refereeing decisions at the moment, and for me it was a definite penalty," said Taylor.
"If it wasn't a foul, why was he touching him?
"I thought we had some good spells but we have to make sure we don't get frustrated when it is 0-0 because 0-0 is not a bad result at this level."
Stoke manager Johan Boskamp admitted that it had not been a great game, and added: "We gave the ball away too easily in the first half but in the second half we got a bit better, and I am very pleased with the character of my team."
Hull bossed the first half and Stuart Elliott missed two close-range chances, before Damien Delaney headed the ball against the crossbar.
However, Stoke fought back in the second half and after Mamady Sidibe nodded against the woodwork himself, Gallagher notched the winner when he turned home Harper's low cross from the right.