Kevin Lisbie and Scott Cuthbert gave O's a two-goal lead before David Amoo's reply from a penalty before the break, coming after Lee Miller's sending off for a foul on Nathan Clarke just after the half-hour mark.
However David Mooney and substitute Dean Cox, twice, made it convincing for the Londoners in the second half.
Orient had the better of an incident-packed and often ill-tempered opening half, twice getting the better of the Carlisle defence with headed goals from set-pieces.
Lisbie opened his account midway through the first half, glancing in Clarke's long throw from the touchline.
There was a seven-minute injury hold-up when Clarke was felled by Miller's challenge deep inside the O's half near the left hand corner flag, which resulted in Miller's red card.
With Clarke replaced by Elliot Omozusi and Carlisle down to 10 men, Orient added to their lead in the 37th minute when Cuthbert rose highest in the penalty area to thump home a header from Lloyd James' corner.
Carlisle got back into it in the 43rd minute when Mathieu Baudry handled a Josh Gillies drive inside the area and Amoo marked his debut for the Cumbrians by converting the resultant penalty.
But the visitors were rocked in the 70th minute when Moses Odubajo squeezed in a cross which found the inrushing Mooney, whose header from six yards left Mark Gillespie helpless.
Orient made it 4-1 in the 81st minute when Cox, on in place of Shaun Batt, curled a low right-footed effort beyond Gillespie from just inside the area.
And Cox was on target again in injury time with another sweet effort which found the net off the underside of the crossbar.