Two of the division's best teams cancelled each other out for long periods at Griffin Park but the crucial goal was scored late in the first half by Marcus Bean.
The central midfielder pounced when a Sam Wood free-kick was not properly cleared by the visitors' defence and he volleyed home from ten yards.
Bury fought for a way back into the game but lost midfielder Stephen Dawson to a second-half red-card for two bookable offences.
The combative player was booked for an aerial foul on Kevin O'Connor which left the Brentford player having to play the rest of the match with a head bandage.
And he was shown a second yellow ten minutes later for kicking the ball away.
Brentford had started the brighter and O'Connor and Jordan Rhodes went close early on but Bury thought they had scored on the half hour.
A Mike Jones corner flew across the face of goal and Brentford goalkeeper Ben Hamer managed to gather, with Efetobore Sodje in close proximity and Bury appealing that the ball had already crossed the line.
Jones also forced a save from Hamer with a far-post volley and Andy Morrell and Elliott Bennett also went close for the visitors.
But Bury keeper Mark Tyler was the busier, making two fine saves from the division's top scorer Charlie MacDonald.
Alan Bennett and Nathan Elder also went close for the home side late on but a fourth successive clean sheet and Bean's goal was enough for them.