Back from their two matches in Belfast, Jon Weaver fired Coventry ahead with a powerplay goal on 4.32, assisted by Robert Farmer.
Brad Cruickshank got a game ban and five minutes for roughing with Aivars Gaisins before Hull equalised on 31.00 through Jereme Tendler.
Coventry were back in front thanks to Arron Nell scored an even handed goal on 36.47, assisted by Dan Carlson and Robert Farmer.
Tendler made it 2-2 with an unassisted short handed goal on 38.32 and with no more goals, the match went into over-time.
Only ninety seven extra seconds were needed before Greg Owen smashed in the winner, assisted by Dan Carlson to give The Blaze the victory.
Coventry Blaze have a training session for season ticket holders on Thursday night before travelling to Hull on Saturday and taking on the Nottingham Panthers at the Sky Dome on Sunday.