A double from David Mooney and further goals by Lee Cook and Ben Chorley exposed major failings in Carlisle's defence although Peter Murphy did briefly bring the home side level.
Three half-time substitutions brought about an improved showing from Carlisle, but the Londoners, with just 13 goals in the league prior to this game, never looked likely to be caught.
Carlisle, who have the worst defensive record in the division, found themselves a goal down in the 18th minute when Mooney headed Dean Cox's right-wing cross against the post and sidefooted home the rebound before Murphy levelled for Carlisle in the 25th minute with a header from eight yards after Jon-Paul McGovern's free-kick had been only partially cleared.
But Orient were back in front within a minute, Chorley supplying the final touch from close in after Lee Cook's corner from the right and in the 38th minute Kevin Lisbie got the better of Mike Edwards and raced through to square the ball across the six-yard box for Cook to tap home unchallenged.
A fourth was to follow in the 44th minute when again shocking defensive play by Carlisle let in Mooney, who raced clear to thump home a shot from just inside the area.