Matthew Lockwood's 10th goal of the season salvaged a point for Orient to deny Carlisle victory at Brisbane Road.
The hosts began brightly and Ryan Jarvis was twice foiled by Carlisle keeper Keiren Westwood early on.
However, Carlisle took the lead when Joe Garner headed in and John Mackie had to clear off the line from Karl Hawley to keep Orient in the match.
But, Lockwood drilled home two minutes into the second half to keep the hosts' hopes of League One survival alive.
Leyton Orient: Garner, Miller, Thelwell (Tann 45), Mackie (Barnard 68), Lockwood, Tudor, Easton, Chambers, Corden (Demetriou 82), Alexander, Jarvis.
Subs Not Used: Morris, Walker.
Booked: Easton, Lockwood, Corden.
Goals: Lockwood 47.
Carlisle: Westwood, Raven, Livesey (Gray 46), Murphy, Aranalde, Gall (Holmes 90), Thirlwell, Johann Smith (Joyce 46), Jeff Smith, Hawley, Garner.
Subs Not Used: Williams, Krause.
Booked: Raven, Hawley, Garner.
Goals: Garner 15.
Ref: R Shoebridge (Derbyshire).