Trotta opened the scoring for the visitors on the stroke of half-time with a low shot from the edge of the box and the Bees held on for the victory despite going down to 10 men.
David Mooney went close for Orient early on but his hooked shot was blocked from close range and Dean Cox then fired just wide from 20 yards out.
Brentford almost opened the scoring on 23 minutes but Clayton Donaldson's shot was saved by onrushing Orient goalkeeper Eldin Jakupovic.
There was an on-field bust-up between the players in the 38th minute after Romain Vincelot and Gary Sawyer's challenges on Brentford's Adam Forshaw.
Sawyer and Bees striker Donaldson - who had raised his hand in the melee - were both booked by the ref.
Trotta then struck for the visitors in the 45th minute with a low strike.
Brentford suffered a blow early in the second half when James Tarkowski earned a second yellow card after bringing down Vincelot.
Orient then went close but Alan McCormack headed clear a cross before Kevin Lisbie fired high and wide from 12 yards out.
O's skipper Nathan Clarke was lucky not to get booked when he pulled down Donaldson on 63 minutes and then got away with it again when he fouled George Saville in the box.
Orient sub Shaun Batt had a shot saved before the winger's header was cleared on the line by McCormack as Orient searched for an equaliser.
But Brentford held on for a crucial victory, with Alan Judge almost adding a second for the Bees when his angled drive hit the post in the closing stages.