The midfielder glanced home Jim McNulty's cross from 12 yards, but the result was harsh on Exeter, who had dominated for long spells.
The first half belonged to the Grecians, but for all their pretty football, clear cut chances were few and far between. Marcus Stewart headed straight at Peter Brezovan inside the opening minute and the experienced striker went close again when his left-footed shot rolled narrowly wide of the far post.
The Grecians really should have gone in front three minutes after half-time when Stuart Fleetwood was upended inside the box by Brezovan. However, Stewart's penalty was poor and the goalkeeper guessed correctly to keep the weak spot kick at bay.
Exeter continued to dominate after the break, but Brighton defended well. The Seagulls had a chance on the break when Liam Dickinson shot across goal, but Andy Marriott got down well to save.
Adam Stansfield fired straight at Brezovan when through on goal and it was left to Crofts to steal the points with that late goal.