A first-half goal from Orient striker Jonathan Tehoue grabbed the Londoners a vital win to keep their play-off hopes alive.
Carlisle has cause to rue an early penalty miss by James Berrett and despite having most of the play, the visitors looked the more dangerous side on the break.
The home side should have been in front in the eighth minute when Craig Curran was bundled off the ball, but Berrett's penalty lacked pace and power and Orient goalkeeper Lee Butcher dived low to his right to save.
Orient took the lead against the run of play in the 37th minute when skipper Stephen Dawson fed Dean Cox inside the Carlisle half and his inch-perfect pass was drilled home by Tehoue from the edge of the penalty area.
Carlisle continued to have the lion's share of possession, but Orient's Adam Chambers showed them the direct approach with a snapshot from outside the box which thumped against the foot of Collins' right-hand post.
Orient had to survive an injury-time scare when home substitute Rory Loy headed just wide from Berrett's cross.