The Cumbrians finished with 10 men after goalkeeper Mark Gillespie saw red for his second bookable offence.
He had been booked for handling outside the area in the first period and then he brought down striker Charlie MacDonald in the 66th minute and was dismissed by referee Simon Hooper - but by then the home side were already two goals ahead.
Romain Vincelot opened the scoring after 32 minutes when he met a perfect cross from Dean Cox to power the ball past Gillespie and on the stroke of half-time Shaun Batt doubled Orient's lead when he stabbed home a cross from Lee Cook.
Substitute MacDonald had raced clear when he was brought down and after Gillespie's dismissal, Kevin Lisbie stepped forward to coolly slot home the penalty past replacement keeper Adam Collin.
Although the visitors pulled a goal back through a superbly-struck shot by Robson, Orient completed a 4-1 win over Carlisle for the second time this season when Cox volleyed the ball home with two minutes remaining.