The impressive Jamie Clarke gave the visitors an early lead before Matt Gill equalised in first-half injury time.
Ben Watson hit the winner for the Grecians midway through the second half of an entertaining game.
Accrington started brightly and created a string of early chances. Paul Mullin deflected Peter Cavanagh's free-kick towards goal in the opening minutes, but could only find the arms of Paul Jones.
Clarke had a low shot saved by Jones and John Mullin struck the ball over the bar as the visitors pushed forward.
The inevitable happened when Clarke controlled a long ball, cut in from the right and steered a low drive past Jones from 15 yards.
Kenny Arthur then prevented Exeter from equalising with an extraordinary double save. Ryan Harley's fine volley from Richard Logan's pass was well blocked by the goalkeeper and when the ball rebounded to Marcus Stewart, Arthur spread himself superbly.
Clarke again went close for Accrington after bursting into the box and shooting wide.
The Reds almost doubled their lead when John Miles curled the ball against the crossbar from the edge of the box with Jones beaten.
But Exeter levelled deep into injury time when Dean Moxey's long throw was flicked on by Logan and Gill tapped the ball home at the far post.
After the break Logan should have put Exeter ahead when he pounced on an error by Phil Edwards but failed to connect with the ball.
The Grecians took the lead midway through the half when Harley's fine ball picked out Watson, who steered the ball past Arthur with a fine finish from ten yards.
Stewart and Harley both tested Arthur late in the game, but Exeter had done enough for a morale-boosting victory.