The Bees comfortably won 3-1 to stay in the frame for automatic promotion.
Goals by Paul Brooker and Marcus Gayle in the first half and a late killer blow by Calum Willock settled the game.
The disappointing result left Swindon second bottom with only two games left to save themselves.
The first half started off in a very lacklustre fashion with both teams unable to carve out any decent openings.
But that all changed in the 27th minute when Brooker picked up a loose pass on the edge of the Brentford area and ran fully 70 yards before tucking the ball under Rhys Evans in the Swindon goal.
The goal seamed to knock the stuffing out of Swindon and it was no surprise when they conceded a second just before half-time.
A long punt by Stuart Nelson caused panic in the Swindon defence and Evans collided with his own defenders leaving Gayle free to stroke the ball into the empty net.
The Swindon fans invaded the pitch shortly afterwards and threw their shirts to the ground in disgust before being led away by the stewards.
After the break Swindon had two strong penalty claims turned down.
Substitute Aaron Brown got Swindon back into the game with a quickly taken free-kick that caught the Brentford goalkeeper by surprise.
Swindon then pressed but could not find an equaliser and it was Brentford that had the last say in the matter.
Another comedy error in the Swindon goal by Evans colliding with his own defenders left Willock with an easy chance to wrap up the points.