Bolton had the first chance of the match but Kevin Davies's header landed the wrong side of the post to let off Hull early on.
However, Owen Coyle's side did take the lead a few minutes later through Chris Eagles.
The attacking midielder's free kick took a deflection to leave Ben Amos with no chance as the visitors got the goal that their early play deserved.
Hull started to enjoy longer spells of possession before the break and Sone Aluko equalised before half time with a shot that hit Tim Ream on its way into the back of the net.
The hosts finished the better of the two sides in the first half and Jay Simpson should have put his side ahead but the striker's header from close range was off target.
Hull extended their lead further just three minutes later as Jay Simpson evaded two defenders before pulling the ball back to Quinn, with the midfielder applying a simple finish.
Seyi Olofinjana was close to scoring a fourth for the Tigers but his free kick hit both posts before being cleared to safety by a desperate Bolton defence.
Marvin Sordell could have pulled a goal back for Bolton but the substitute's header was wayward and failed to trouble Amos.