Torquay United lead in the Devon derby after Rene Howe slotted away a 12th-minute penalty past Artur Krysiak.
The Gulls started the better of the two teams, with Lee Mansell testing Krysiak with an early header.
Former Torquay United player Steve Tully then gave away a soft penalty as he clipped the heels of Billy Bodin just inside the area, with the Torquay player heading into a crowd of Grecian players.
However, referee James Adcock was well placed to award the penalty and Howe slotted home.
After that Exeter City got a foothold in the game and were unfortunate not to equalise when Jimmy Keohane shot narrowly wide of the post. Keohane also had another effort blocked from close range, while the impressive Mark Molesley shot straight at Michael Poke from the edge of the area.
Paul Tisdale has a number of options on the bench to call from in a bid to get his side back into the match. Leading scorer Jamie Cureton has been named as a substitute, while Guillem Bauza and Jake Gosling are other attacking options.