The Glovers scored inside two minutes but found themselves trailing before half-time and needed a brave second-half fightback to snatch a point.
The early goal came when Andy Williams chested a long clearance into the path of Ed Upson who hammered home from the edge of the box. The lead lasted just two minutes. Scott Golbourne did some good work on the left and laid on a chance for Jake Taylor who rounded the goalkeeper to level.
There were chances at both ends before Exeter took the lead after 30 minutes. Darren Purse pushed John O'Flynn and the striker got up to score from the penalty spot.
Yeovil had more of the second half although City hit the top of the crossbar after 37 minutes when Troy Archibald-Henville moved up for a corner.
After 56 minutes Yeovil levelled when Upson's left-wing corner was glanced in by the head of Dominic Blizzard. Only the brilliance of Arthur Krysiak in the City goal then denied Paul Wotton what would have been the winner.