The centre-back smashed home a loose ball in the box as the Bees failed to clear to give the Terriers three points they barely deserved.
Neither side looked potent in front of goal in a game fought out in midfield.
Former Brentford striker Jordan Rhodes came closest for the visitors in the first half, forcing a full-length save out of Richard Lee from his curling effort from the edge of the box.
The closest the hosts came to breaking the deadlock was two minutes after the restart when Miles Weston's rasping drive was palmed away by Town keeper Alex Smithies.
Brentford almost went ahead after 81 minutes when on-loan Leicester striker Jeffrey Schlupp almost scored with his first touch but his effort was blocked, leaving Clarke to steal the headlines.