The Grecians made the best possible start and took the lead in the third minute through Wayne Carlisle's free-kick. York pulled level through James Dudgeon and ran away with the game in the second period thanks to strikes from Neil Bishop and Andy Bishop.
The teams were well-matched in the first half but York looked much livelier and more decisive after the break and fully deserved to take the points.
Exeter went ahead inside three minutes in bizarre circumstances. Jon Challinor was brought down 35 yards from goal and Carlisle's free-kick bounced wickedly before it flew over the head of the stranded goalkeeper Chris Porter and into the top corner.
Craig Farrell thought he had stretched the lead for the Grecians when he volleyed home from 12 yards but his effort was ruled out for offside.
York were level just after the half-hour. Darren Dunning's cross picked out Dudgeon and the centre-back headed the ball against his own foot before watching it fly into the back of the net.
After the break it was York's turn to grab an early lead. Less than three minutes after the restart Neil Bishop reacted first to Dunning's half-cleared corner and thumped the ball home from ten yards.
Exeter attempted to get back into the game and Dudgeon superbly charged down Dean Moxey's close-range strike. But York always looked the more likely to score.
Clayton Donaldson missed a hat-trick of chances before the Minstermen finally made sure of the points with 20 minutes left.
Dunning's cross to the near post was met by Andy Bishop and the striker's delicate touch from close range was enough to send the ball into the back of the net. There was no way back for the Grecians.