Shortly after seeing his penalty saved with the scores poised at 2-2, Cureton nodded home the 87th-minute winner after Danny Jackman's 30-yarder looked to have sealed a point for the hosts.
Chris Whelpdale had put the Gills ahead after just four minutes, latching onto Lewis Montrose's through ball. Exeter's Liam Sercombe scuffed a great chance to level but Alan Gow made no mistake with a fine free-kick on 27 minutes.
Nine minutes after the break 37-year-old Cureton poked home his 14th of the season to hand the Grecians the lead. Jackman then lashed home on 78 minutes to make it 2-2.
Cureton struck his spot-kick straight at Gills stopper Stuart Nelson after Jimmy Keohane was hauled down in the box, but he made up for it by heading his fifth goal in four games almost immediately.