Andy Williams put Town ahead five minutes before half-time but City hit back through Richard Logan after 75 minutes.
Exeter almost went in front early on, but James Dunne's shot crashed back off the underside of the crossbar. Yeovil's Steve MacLean also hit the woodwork when he latched onto a long ball forward - his chip landed on top of the bar.
The visitors took the lead when goalkeeper Artur Krysiak completely missed his attempted punch and Williams headed into a gaping goal.
The hosts levelled things up with their first effort on target. Substitute Guillem Bauza played a fine through-ball to Logan, who rolled his shot under the advancing Rene Gilmartin.
Bauza almost won it for Exeter in stoppage-time but he dragged his shot wide.