There was 12 minutes left when Lloyd Owusu grabbed the points from a corner to bring Brentford a 15th league win and their third in a row.
For Bristol the defeat has plunged them back into the relegation dog fight.
For a long time the game stuttered from one free-kick to another - most of them in the first half going Bristol's way while Brentford made more of theirs.
There was an early scoring chance for the London side when Jay Tabb was brought down just to the left of the penalty area. Kevin O'Connor curled that one a foot over the top.
Darren Pratley took the next and from roughly the same range tried a chip which skipped just past the far post.
The home side were not showing anything like the same creativity, although when Scott Murray got in a deep cross Stephen Brooker rose well to send a header a fraction high.
It was City's best moment of the first half but Brentford were soon back with Tabb bursting through on the right with a fierce drive and then John Mousinho got in a snap-shot from the same area.
After the goalless and drab opening half there was a need for passion. The stadium announcer did his best to inject a little but it was City manager Gary Johnson who finally roused the fans.
He made two quick substitutions in the second half and a loud cheer greeted the arrival of former Sunderland striker Marcus Stewart who has found himself frozen out in recent months.
But the pressure was soon back on City and a corner was again their undoing.
Owusu found space on the edge of the six-yard box to hook in Pratley's flag-kick from the right.