Managerless Orient grabbed three precious points in this basement battle after Carlisle had scorned a string of scoring chances.
Jabo Ibehre punished an awful defensive muddle in the 66th minute to secure the Londoners' first win at Carlisle for 16 years.
There did not seem to be any danger as Tom Newey over-hit a diagonal through ball but home defender Peter Murphy and keeper Matty Glennon dithered and got in a tangle as the tall striker stretched out a leg to poke the ball home from 10 yards.
Orient's defence looked fragile as they survived an early blitz. Simon Downer rescued them in the fifth minute with a goal line clearance, when Richie Foran raced clear and rounded keeper Lee Harrison before shooting towards an empty goal.
Foran fired tamely wide with only the keeper to beat after 24 minutes and three minutes later midfielder Chris Billy was put clean through but Harrison beat away his shot.
On the half hour, after having their backs to the wall, Orient broke quickly and came close to an opener - Gary Alexander meeting Wayne Purser's cross with a powerful eight yard header that flew wide.
Then, Purser saw a 12 yard effort deflected past the post when Glennon dropped the ball under pressure from Alexander's aerial challenge.
As Orient settled Alexander blazed over the bar from the edge of the box when a hopeful through ball bounced kindly for him off a home defender.
But it was not until a minute into the second half that the visitors managed a shot on target - an angled drive from Ibehre that Glennon pushed round the post.
Foran had the ball in the net after 61 minutes but the flag was up.
Then Ibehre stunned the home fans and Carlisle ran out of steam.
They had hopeful penalty appeals turned down in the 78th minute when Mark Peters appeared to handle a Foran header.
But a measure of their desperation was the 86th minute substitution of winger Brendan McGill, with centre back Darren Kelly coming on to try to add some weight up front.
Afterwards, Orient's caretaker-boss Martin Ling said: "Things are tense at the moment and we rode our luck in the first 15 minutes.
"It was a scruffy goal but it's a step in the right direction."