The Bees played the inexperienced pairing of Osei Sankofa and Karleigh Osborne at centre-back and it really showed.
Two goals in two minutes before the game was a quarter of an hour old killed the contest off and both were schoolboy errors by the Bees.
Nicky Adams opened the scoring on 13 minutes after a mix up between Sankofa and Osborne which looked to have come from a lack of communication.
Glynn Hurst made it 2-0 just two minutes later when Bury were allowed to play the ball at will through the midfield and Osborne was beaten for pace.
It was game over seven minutes before half-time when another catastrophic error saw Andy Bishop add Bury's third.
Home keeper Ben Hamer had seemed in little danger when he received a back pass, but it went straight to Bishop who chipped it back over him.
Bees boss Andy Scott rung the changes at half time, taking off Sankofa and Wayne Brown for Ricky Shakes and Reuben Reid in a desperate effort to get back into the game.
The breakthrough came on 55 minutes just after Nathan Elder had had a header cleared off the line.
From the resulting corner, Efetobore Sodje handled on the line and Glenn Poole dispatched the resulting penalty.
Five minutes later Hurst reminded Brentford of the danger down at the other end when he forced Hamer to make a fine save with his feet.
As much as the Bees pushed forward they didn't find a second goal that would have brought them back into it.
Instead, Bury scored a fourth that killed the game off eight minutes from time.
Bishop took advantage of more gaps in the Bees back four to fire home and clinch victory for the visitors.