From the kick-off Barnet scored with a crisp passing move, the climax of which was a deep cross from Dean Sinclair, finished by Giuliano Grazioli with aplomb at the far post after only 15 seconds.
After the opener the game was keenly contested and bruising challenges were traded.
The Bees had the best of chances in the first half. After half an hour Louis Soares cut inside and fired a testing shot inches wide.
Minutes later Grazioli almost scored his second as he just failed to connect with an Ian Hendon throughball.
However, the hosts were made to pay just before half-time, as the strong Jabo Ibehre, put back in the Orient team after recovering from a knee injury, finished off a sweeping move by putting the ball in the back of the net.
Barnet had a goal disallowed on the stroke of the half.
After the break, Orient took the initiative, but struggled to make a breakthrough.
Gary Alexander eventually found himself in space to put the away side 2-1 ahead on 75 minutes with a cool finish.
In the second half, Barnet looked tired and gave the marauding Orient forwards too much space in which to move.
Alexander capitalised on this space again after 89 minutes with another clinical finish.
With the game all but over Orient relaxed, allowing Grazioli to score his second from close range just before the referee blew for full-time.
Orient's second half dominance should have provided more goals, while the scoreline flattered the home team.