Two late goals from substitutes mean that Town stay one place below their opponents in the current play-off race.
Salop took the lead early in the second half, when Lee Lawrence volleyed home from just inside the box after Martin O'Connor's corner was not cleared properly. The second came on 71 minutes when Duane Darby hooked home after another Martin O'Connor corner.
The first half had been a scrappy affair, with neither goalkeeper properly tested. The second period began well for Town with the on-loan Man Utd youngster Lawrence looking lively on the left, despite being anonymous before the break.
Exeter made changes after going 2-0 down, and they paid off when Dean Moxey scored with practically his first touch after a free kick on the right.
Then, just 90 seconds before the end, another centre resulted in late sub Steve Flack turning the ball past keeper Steve Howie.
Town had been dangerous from corners all afternoon and could have grabbed the points at the end after a scramble on the edge of the box.
Town: Howie (6), Challis (7), Sedgemore (5), Tinson (6), Ridler (6), Lawrence (7), Lowe (6), Street (5), O' Connor (7), Banim (7), Darby (7)
Subs: Rodgers (6) For Banim, Cramb (7) For Darby, Not used: Hart, J. Tolley, Edwards.
Attendance: 4185