The game was largely dour with neither team really grabbing it by the horns, although in the fifth minute Gary Alexander managed to head over the bar.
However, five minutes later at the other end Justin Walker's free-kick was deflected by Ian Ashbee and Paul Musselwhite had to make a good save low to his right to save the Hull City captain's blushes.
In the 15th minute Kevin Miller held Steve Melton's shot before Alexander found himself in a great position ten yards out but poor control let him down and his effort spiralled away for a throw-in.
From Andy Holt's long throw Daniel Webb headed straight into Miller's arms.
In the 17th minute Hull looked sure to score through Alexander's point-blank header at the far post but an amazing save by Miller low to his left somehow denied him.
A couple of minutes later Martin Thomas' free-kick was held by Musselwhite before Stuart Green aimed a right-wing cross straight at Miller when the advancing Webb was completely unmarked.
Alexander had a couple more chances before Carl Regan's low shot was kicked off the line during a spell of pressure by the Tigers.
After the break, the pace slowed even further, although the Grecians' Santos Gaia shot over the bar after being given acres of time and space.
Hull finally took the lead in the 61st minute when Green delivered a pin-point cross from the left wing to the head of Stuart Elliott about ten yards out in a central position.
Elliott's trademark celebration of a triple summersault was seen again only six minutes later when he slotted home from an acute angle 20 yards out.
But Exeter immediately hit back and substitute Scott Partridge silenced the home fans by taking advantage of a defensive error and bundling the ball past Musselwhite from close range.
The Tigers still looked the more assured side and would have been odds on for a win especially when Graeme Power was given a straight red card for bringing down Lawrie Dudfield who was through on goal.
But there was still time for Exeter to have the last laugh. In almost identical fashion to their earlier goal Steve Flack broke free and scored from close range to the delight of the few Exeter fans dotted around Hull's vast North Stand.