After a scrappy start, the visitors went in front with a goal on the counter-attack after 19 minutes. Ashley Chambers broke clear down the right and after Artur Krysiak had saved from Lewis Montrose, Ryan Jarvis tapped in the rebound.
The Grecians then lost John O'Flynn to injury on 22 minutes, but within 30 seconds of replacing him, Gow had Exeter level as he beat the offside trap and finished superbly with his left foot.
The Minstermen looked threatening on the break and should have gone in front when Michael Coulson found himself in plenty of space, but he shot tamely wide of the near post.
Gow put Exeter in front 17 minutes from time when he received the ball 25 yards out and lashed a stunning shot into the corner of the net that gave goalkeeper Michael Ingham no chance.
York almost levelled yet Coulson poked straight at Krysiak from six yards, and that was as close as they came as Exeter held on.