The O's maintained their unbeaten start to the season as Barnet's winning run comes to an end in East London.
It was the hosts who started well, McAnuff and Koroma both having efforts at goal in the opening ten minutes, the first saved by Cousins and the second off target.
The Bees first chance came nine minutes in when good inter-play between Elliott Johnson, making his 200th appearance for the Bees, and Jack Barham eventually found Josh Walker but he shot over the bar.
Leyton Orient would take the lead in the 11th minute from a free kick routine which saw Josh Coulson slide in to convert Charlie Lee's header back across goal.
Their advantage would last just 13 minutes however as Wes Fonguck hit a superb half-volley past Brill after David Tutonda's knockdown for his second goal of the season.
Johnson delivered a good cross from the left shortly after the half hour mark but it was headed away by Coulson just before it reached Barham.
Barnet had performed well in the first half but, after the break, Orient came out fighting and Coroma delivered a good cross from the right but there was no one in red on the end of it.
Fonguck looked to double his tally soon after, bringing the ball forward to the edge of the box before hitting it left-footed into the arms of Brill.
Justin Edinburgh rolled the dice on the hour, making a double change and this injection of energy paid off when they retook the lead in the 68th minute.
Barnet lost possesion in the midfield, allowing Orient to counter and race down on the Bees goal. Craig Clay set up James Dayton and he hit a fine curling effort into the top left giving Cousins no chance.
Several golden chances for Alabi came and went before the hosts bagged a third, Macauley Bonne initially striking the upright from close range before tapping home the rebound.
It was damage limitation here on in, with wave after wave of Orient attack and with all subs made, Johnson picked up a minor knock and was moved up front.
The Bees never looked like getting another goal but came close in injury time when Charlee Adams' low volley had Brill scrambling but it went narrowly wide.
Barnet - Cousins, Alexander, Johnson, Robson, J. Taylor, Fonguck (Kyei 79), Walker (Mason-Clark 66), Tutonda (Payne 69), Sweeney, Barham.
Unused - Matrevics, Sparkes
Attendance - 5,601 (610 Barnet)