The visitors looked set to snatch the win despite being second best throughout before succumbing to the home side's pressure.
Gary Smith, Karleigh Osborne and Sam Williams combined to set up David Hunt and his low cross was turned home at the far post by Clarke for the last-gasp leveller.
The young forward was villain-turned-hero as he had earlier seen a penalty, awarded for hand-ball by Matt Gill, saved low to his left by Exeter goalkeeper Paul Jones.
Jones had spent most of the day denying the home side and after Stuart Fleetwood struck a breakaway goal late in the first half, it looked like Exeter would take the points.
Fleetwood had created the goal out of nothing by picking up a Troy Archibald-Henville pass nipping inside Osborne and slotting home.
But that was almost all they created as Brentford dominated.
The home side had a goal ruled out inside the first ten minutes, when Damian Spencer's far-post header from a Hunt corner was disallowed as the assistant referee decided the ball had swung out of play.
Jones saved well from a Spencer header before smothering at his feet and he also tipped a Hunt free-kick around the post.
He also saved well from Spencer again when a low shot looked set for the far corner and Brentford captain Alan Bennett also flicked a header inches wide.
Hunt curled a free-kick just past the post and Jones saved from Osborne as Brentford fought for a leveller.
It looked as if it wasn't going to come, but Clarke popped up with seconds remaining.