The Bees took the lead in the sixth minute when Marcus Bean controlled with his right foot and curled an unstoppable shot past the outstretched arm of goalkeeper Jamie Jones with his left.
The home side extended their lead midway through the first half when Myles Weston slipped his man at the byline to cross low for Gary Alexander to smash home into the roof of the net from close range.
But the visitors emerged more purposeful after the break and hauled themselves back into the game on 55 minutes when veteran striker Scott McGleish pounced on a moment of hesitancy in the Brentford box to slot home from five yards.
The defeat was a big blow to Orient who would have set a club record had they managed to clinch a draw, but a string of fine saves from substitute keeper Simon Moore denied Adam Barrett and Alex Revell in the closing stages.
The only downside for Brentford came just before the break when goalkeeper Richard Lee was taken off with what looked like a suspected fracture to his arm which puts him in doubt for the Johnstone’s Paint Trophy final at Wembley next month.