Jabo Ibehre gave the Dons the lead midway through the first half when he capitalised on some sloppy Exeter defending to lash home a loose ball from 12 yards.
Ibehre had already had one effort at goal by then, lobbing the ball wide of the far post after a mistake by Troy Archibald-Henville.
Exeter had played plenty of good football in the opening 45 minutes and Nicholas Bignall missed their best chance on the stroke of half-time. He headed wide from six yards with the goal at his mercy after some terrific play by Liam Sercombe down the right wing.
Exeter enjoyed long spells of possession in the second half, but a striker shortage meant they lacked an end product.
There was plenty of probing from the Grecians with the Dons playing on the counter-attack and in the last minute Dean Bowditch beat Exeter’s offside trap to run through and slip the ball under the goalkeeper.