Carlisle's point came at a cost after striker Scott Dobie was dismissed three minutes from time for lashing out at O's defender Brian Saah. Carlisle, unchanged for the fourth successive game, started well and carved out some early half chances, but Orient gradually came back into the game and Jason Demetriou saw a snapshot defected inches wide.
But the visitors should have scored on 26 minutes when the ever dangerous Simon Hackney crossed from the left and Dobie headed wastefully over from inside the six-yard box. Orient responded and Paul Terry came within a whisker of scoring his first goal for the club but saw his shot drift tantalisingly wide.
Adam Boyd then flashed a header past the post before Ben Williams, in the visiting goal, saved superbly from Orient substitute Simon Dawkins after the on-loan striker raced clean through. After the break both sides played some excellent football but it was Orient who created the cleaner chances. Ryan Jarvis headed inches wide and then blasted an effort over the bar from 20 yards.
However, Carlisle always posed a threat on the break and Glenn Morris saved well from Danny Graham. Boyd almost broke the deadlock with a speculative shot as Orient threw caution to the wind and Williams saved bravely at the feet of Adam Chambers. But Carlisle still threatened on the break as substitute Cleveland Taylor hit the top of the bar with a looping header, but when Dobie was dismissed any hopes of sneaking a late winner disappeared.