Jon Maloney put York ahead, only for Jake Edwards and then Lee Phillips to give the Grecians victory with all three goals coming from corners.
The visitors were anxious to get back to winning ways to recharge their play-off challenge and started the game with an adventurous 4-3-3 formation. The tactic almost paid off in the second minute when Phillips headed just over with a free header from a left-wing cross.
The Minstermen soon got on top, and played some attractive football in the first half and created a number of openings.
The best early chance fell to Dave Merris who received Andy Bishop's pull-back but sliced his left-foot shot wide from a good position. Then Darren Dunning's cross from the left picked out Bishop at the far post, but his header struck the top of the bar.
York went ahead on 38 minutes from Kevin Donovan's corner which keeper Paul Jones punched backwards under pressure and Maloney headed his second goal in successive games from close range.
Exeter equalised in first-half stoppage time from a corner of their own. Alexandre Jeannin's accurate inswinger was flicked home by Edwards at the near post from six yards.
After the break the visitors took total charge dominating possession and keeping the Minstermen pegged in their own half.
On 52 minutes Andy Taylor's cross from the right was left by Paul Groves for Chris Porter but Phillips nipped in between only to be wasteful with his effort on goal.
The Grecians' pressure paid off eventually as they went ahead on 63 minutes. Once again it was Jeannin's inswinging corner which Phillips headed in at the far post.
York boss McEwan gave on-loan striker Ben Jackson his first start following his loan move from Doncaster on Friday. Paul Robinson then replaced Dunning as City moved to a 4-3-3 formation in search of an equaliser, but they failed to test Jones in the Exeter goal throughout the second period.