Hull got off to a flying start when after only six minutes, Damien Delaney's left sided cross caused mayhem in the area with Marlon Broomes' attempted clearance striking the heels of Darel Russell to give away the goal.
Stoke finally got up and running after 17 minutes when Carl Hoefkens' long ball out to the right found Luke Chadwick who crossed for Michael Duberry who sent his header screaming over the bar.
The home side gathered more confidence and finished the half strongly but an equaliser still eluded them as Paul Gallagher's attempted 20-yard strike was scuffed and never threatened Boaz Myhill's goal.
Hull's slim lead survived by a thread five minutes after the break when former Port Vale centre-back Sam Collins brought down loanee Gallagher inside the box to give away a penalty.
However, the Scottish striker's spot-kick was struck almost directly down the middle giving Myhill the opportunity to palm the ball away for the clearance.
Jon Parkin doubled the Tigers' lead in the 55th minute when he was given acres of space eight yards from goal which allowed him to coolly slot the ball past a helpless Steve Simonsen.
Stoke seemed destined to lose as referee Andy D'Urso gifted the Potters a second penalty kick in the 65th minute when Jon Welsh's high foot caught winger Peter Sweeney.
After having a torrid afternoon, Gallagher stepped aside allowing Chadwick to take but yet again Myhill stood strong and caught the poor effort.
Hull rounded off their afternoon in style with Craig Fagan supplying a pin-point through ball for substitute Darryl Duffy who had no hesitation in placing the ball into Simonsen's bottom left corner from 10 yards.