Hull goalkeeper Matt Duke, making his first start of the season due to Boaz Myhill's suspension, enjoyed an easy start to the game as both sides struggled to find the target in the first half.
He was brought into action on the half-hour mark as Cardiff piled on the pressure with skilful and determined play from Jason Koumas, resulting in a sharp shot from 18 yards being turned away by the Tigers keeper.
Koumas had another chance minutes later, but this time dragged his shot wide of the post from outside the area.
Cameron Jerome fired a decent chance from inside the area well over the bar on the stroke of half-time and within a minute of the second half Koumas again tested Duke's reflexes with a curling free-kick.
Hull fought back soon after and a brave block from Purse prevented a well-struck Paynter volley from putting the Tigers ahead.
Cardiff then had another chance to take the lead from a free kick as Koumas fired just wide from the edge of the area.
However it all fell apart for the Bluebirds as they were reduced to ten men with skipper Purse receiving a second booking after a tackle from behind on Fagan.
Hull pushed forward immediately after and some good work from Fagan down the right flank resulted in a curling cross, which striker Paynter managed to get on the end of, beating Cardiff keeper Neil Alexander to the ball to put his side into the lead.
Cardiff came very close from a Koumas free kick which was tipped over by Duke but Hull made sure of the win in the closing stages.
A superb crossfield ball from substitute Stuart Elliott put Fagan through on goal and he made no mistake as he slotted the ball past the oncoming Alexander.