The Londoners took advantage of some poor Carlisle defending to open up a three-goal lead. Charlie Daniels, Scott McGleish and Simon Church all found the net for the visitors, with Scott Dobie netting a late consolation for the home side.
United started with top scorer Danny Graham on the bench, with the striker nursing a groin injury. Key defenders Peter Murphy and Danny Livesey also missed out through injury.
The void they left was filled by David Raven and Richard Keogh.
United started the brighter, with Joe Anyinsah missing a glorious chance to put the Cumbrians in front. His sweetly struck shot from six yards out hit keeper Jamie Jones and flew to safety.
Five minutes later midfielder Graham Kavanagh had another chance but his side-foot shot was smothered by Jones.
As the early enthusiasm faded Orient got more into the game and had chances of their own.
Both Jordan Spence and Church tested Ben Williams from the edge of the box, but the keeper was equal to both shots.
On 29 minutes the deadlock was broken. Carlisle failed to clear a corner from Jason Demetriou and when McGleish rolled the ball to Daniels he hammered it past Williams into the far corner.
Orient doubled the lead on 35 minutes when veteran striker McGleish, on loan from Wycombe, flicked a Jimmy Smith cross into the corner giving Williams no chance.
Carlisle's terrible defending was to blame as no-one picked up McGleish who had bags of time to pick his spot.
Smith was a thorn in Carlisle's side all game and the winger, on loan from Chelsea, again showed his class when he crossed for McGleish, but his volley went over the bar.
Greg Abbott brought on Graham at half-time for Cleveland Taylor but the marksman didn't really get into the game.
Orient made sure of the points on 50 minutes when the tricky winger Smith darted into the box and crossed for Church to slam home the third.
Strikers Dobie and Gary Madine replaced Gareth Taylor and Anyinsah and it was former Scotland international Dobie who pulled a goal back with 12 minutes left.
A scuffed shot from Graham found Madine, who passed it sideways for Dobie to finish from 15 yards.
Carlisle rallied late on but could not find the target again.