Debutant Chris Dickson put the visitors ahead with 10 minutes gone after he outmuscled Brentford defender Alan Bennett to lash home.
Midway through the half it was two as Dickson again raced down the right and lobbed Bees goalkeeper Lewis Price from 20 yards.
Striker Aaron Lescott stretched the lead just before the break when he finished off a flowing counter-attack to slide the ball home from the edge of the box.
Charlie MacDonald reduced the arrears after the break when he lashed home the goal of the game from 30 yards.
Visiting goalkeeper Mikkel Andersen brought down Steve Kabba when he was through on goal for the injury-hit Londoners but somehow escaped with a yellow card.
But Rovers were good value for the points against a lacklustre Bees, who lacked any real bite in the final third.