After a goalless first half, in which Exeter were denied a clear penalty following Hamsa Bencherif's handball, the Grecians went in front 11 minutes after half-time.
The goal came after a brilliant turn by Alan Gow, who then fed the ball to Arron Davies to smash into the top corner.
Argyle then levelled when substitute Luke Young fired an unstoppable free-kick over the Exeter wall and into the far corner from 25 yards.
But Exeter responded well and Gow put them back in front on 83 minutes with a goal of real brilliance. He received the ball on the corner of the penalty box and curled a superb shot over the head of Luke McCormick and into the net.
Argyle never really threatened an equaliser and Exeter were happy to hit their derby rivals on the break. They were ultimately rewarded in the third minute of stoppage time when Jimmy Keohane crossed for Scot Bennett to turn and roll the ball into the corner to seal a famous win.