Manager Andy Scott was delighted with the manner in which his Brentford players responded to a half-time ear-bashing by ending Exeter's unbeaten home record.
The Bees made it three consecutive wins in npower League One with an impressive away performance.
Leon Legge headed them in front only for Jamie Cureton to equalise. But Brentford hit the Grecians with two quick goals. Gary Alexander got the first when he bundled the ball home from close range after 62 minutes and Sam Wood added a third two minutes later.
More shocking defending from Exeter led to the fourth goal as the Grecians failed to clear their lines and Charlie McDonald rolled the ball into the corner from 15 yards. Cureton headed in Richard Logan's cross for Exeter to make it 4-2, while Kevin O'Connor and Myles Weston missed late penalties for the Bees, which were saved by Paul Jones.
Scott said: "We got the early goal and put pressure on them but after that we looked like we could concede every time they had the ball. It was unlike us defensively and we started to do things wrong.
"The players got a rocket at half-time but they responded magnificently. I said before the game that people will start asking questions of us because we lost after we beat Hull, we lost after we beat Everton and after a good result at Birmingham, I didn't want to continue that run. This is a really tough place to come and they have a great home record. But the way the second half went, they could have had four and we could have had 10. It was that type of game."