York stuck with the 4-4-2 formation which brought them success midweek at Tamworth and could have gone ahead after three minutes.
Andy Bishop was clean through but pushed the ball too far ahead and Billy Jones blocked his effort. Clayton Donaldson showed great skill chipping the ball over Chris Todd's head and volleying just wide.
The lively striker was central in City going ahead when Gary Sawyer pulled him down as Darren Dunning chipped the ball into the box. Bishop stroked the resulting penalty past keeper Paul Jones with his right foot.
Exeter hit back to equalise with their first chance two minutes later, when Steve Flack's stooping header at the far post beat Chris Porter from Billy Jones' free-kick.
This Minstermen hit back to lead when Mark Convery and Donaldson linked to set up Bryan Stewart, who stroked the ball home from 12 yards on 38 minutes.
Exeter made a double substitution at the break and hit back strongly.
Craig Farrell was inches away with a glancing header before the Grecians were awarded a penalty when a York defender was adjudged to have handled in a packed goalmouth following a long throw. Farrell stepped forward but smashed his spot-kick against the base of the right-hand post.
The home side increased their lead with their first chance of the half. Convery cushioned the ball into Donaldson's path and the striker's pace took him clear before thumping home from the edge of the area.
Exeter were awarded another penalty after 73 minutes when DaveMerris and Les Afful fell to the ground together chasing a ball into the area.
Defender Jones took the responsibility to score from the spot.
On 90 minutes Joe O'Neill cleared from deep in his own half to set Donaldson clear from halfway and as keeper Jones blocked, the ball ran loose to Bishop who slotted home into an empty net.