The visitors were always in control as Danny Graham and David Raven struck in the opening 31 minutes and Orient's comeback hopes were crushed when JJ Melligan saw red shortly afterwards.
Carlisle, in cruise control after that, wrapped things up when Grant Smith added a third early in the second half.
Promotion chasing Carlisle could not have wished for a better start as they took the lead on 17 minutes.
Orient paid the price for not picking up their markers as Chris Lumsdon floated in the perfect ball from the right and Graham headed home from close range.
The visitors added a second on 31 minutes when a static home defence allowed Raven to roam into the box and the defender rifled home in deadly fashion.
Any realistic chance of an Orient revival disappeared three minutes later when Melligan was sent off. The O's winger won the ball, but referee Keith Hill had judged the home player guilty of a two-footed tackle on Evan Horwood.
In the melee that followed Orient's assistant manager Dean Smith was sent to the stands and Paul Terry booked.
After the break Orient boss Martin Ling made a double change as Stephen Purches and Jabo Ibehre entered the fray.
However, Smith added a third for the visitors on 49 minutes when he latched on to a ball from the excellent Marc Bridge-Wilkinson and fired across keeper Glenn Morris into the corner of the net.
After that Bridge-Wilkinson might have had a couple of goals, but shot over the crossbar and was then denied by keeper Morris.
Orient tried desperately to stem the flow and created a couple of half chances as Ibehre and Purches shot wide, but Carlisle fully deserved their victory and the three vital promotion points.