Hull took the lead after 31 minutes thanks to Stuart Elliott's shot, but a spectacular overhead kick from Dennis Wise drew Coventry level before Stern John struck 10 minutes later to seal the win.
It was a close game early on with Coventry's Gary McSheffrey having the only real chance in the first 10 minutes but he skied the ball over the bar from 18 yards.
The Tigers then took the lead as both Darryl Duffy and Jon Parkin had shots blocked from the edge of the area and with Coventry failing to clear their lines, a loose ball came to the feet of Elliott who fired it into the roof of the net from the left-hand side of the box.
Hull nearly doubled their lead before half-time as Keith Andrews saw his looping shot come back off the crossbar from 18 yards.
The Tigers nearly extended their lead early in the second half as Duffy found himself with a chance inside the box but the oncoming Marton Fulop did well to bend the striker's shot around the post.
Soon after Hull keeper Boaz Myhill produced two high-class saves to keep his side in front as James Scowcroft saw his shot parried and then from the following corner Myhill saved superbly from a bullet John header.
But the keeper was helpless on 61 minutes as veteran Wise produced a spectacular bicycle kick inside the area to put his Coventry side on level terms.
After continued pressure from Coventry they went into the lead on 72 minutes as a McSheffrey cross was neatly chested into the back of the net by John.
Hull could have levelled the score late on when Ryan France found himself with a chance inside the box after some neat play, but he could only play the ball tamely into the hands of Fulop.