Despite Stoke’s first-half domination, Hull could have had an early penalty when Ashley Phillips slid in and felled Matt Crooks.
The Potters took advantage of that let-off and Thomas hit a right-foot curler towards the top corner, which Hull goalkeeper Ivor Pandur touched away at full stretch.
But Wales international Thomas would not be denied and he gave Stoke the lead with a superb strike on 17 minutes.
Ajayi headed Aaron Cresswell’s corner more up than away and Thomas watched the ball drop perfectly onto his boot, showing excellent technique to fire home the sweetest right-foot volley.
Stoke might have had more and Pandur dived to his left to touch Bae Jun-Ho’s shot around the post and Robert Bozenik had a header chalked off for offside.
Hull made Stoke pay for not extending their lead just three minutes into the second period after some half-time substitutions by Tigers boss Sergej Jakirovic fired up the visitors.
Substitute Mohamed Belloumi looked close to being offside when he flicked on Gelhardt’s off-target shot with what appeared to be the top of his right arm and Ajayi reacted quickest to the loose ball to head in his first Hull goal.
Stoke eventually started to play their way back into the game and Tigers skipper Lewie Coyle made a brilliant goal-saving challenge on Jun-Ho.
Hull finished strongly and substitute John Lundstram wastefully volleyed over before the game’s decisive moment.
Stoke lost possession in their own half, allowing Belloumi to drive forward and lay the ball off for Gelhardt to fire a left-footed shot past Potters goalkeeper Viktor Johansson.