The home side led twice, but were pegged back by Exeter's veteran forward Marcus Stewart, as he bagged a brace.
The visitors started the brighter and almost went ahead on 23 minutes when skipper Dean Moxey smashed a 25-yard free-kick against the crossbar.
Within 90 seconds, the home side got themselves in front. Exeter keeper Paul Jones made an excellent save from a Tom Kennedy free-kick but, from the resulting corner, following a header back across the penalty area by defender Rory McArdle, veteran Lee Thorpe was on hand to nod home.
The home side held sway until the break and indeed just after it, but Exeter equalised on 55 minutes when Stewart bundled home from close range with more than a hint of handball.
The home side thought they had won it on 83 minutes when leading scorer Adam Le Fondre, who had been unable to start the game due to an ankle injury, climbed off the bench.
With his first meaningful touch Le Fondre won a penalty when he was brought down by Troy Archibald-Henville. Jones managed to block Le Fondre's penalty, but the livewire striker followed up to score his 20th goal of the season.
Exeter's response was immediate and within 60 seconds they had a penalty of their own when substitute Stuart Fleetwood was upended by Nathan Stanton.
Stewart calmly rolled home from the spot to ensure that his side went back to Devon with a deserved share of the points.