Rovers had a nightmare start, going behind after just two minutes. Dom Ballard picked up the ball after Connor O'Riordan's loose touch and arrowed a shot into the bottom-left corner from distance.
Orient scored a second goal on 27 minutes. Once again, Rovers' recent failings at set-pieces came back to haunt them. Aaron Connolly played a one-two from a short corner to Charlie Wellens and then unleashed a fierce effort that flew past Ian Lawlor.
Rovers barely threatened in the first half, with Jordan Gibson's header and Billy Sharp's close-range attempt both straight at home stopper Killian Cahill. They were indebted to Lawlor just before half-time, as he made a vital save with his feet to deny Ballard from close-range.
Rovers made two changes amid a tactical rejig after the break but it wasn't long before they were picking the ball out of their net a third time. A punt upfield by Cahill was missed by Ben Close and then Jay McGrath, allowing Ballard to run onto it. He then beat the onrushing Lawlor to the ball before tapping into the empty goal.
Rovers kept toiling in search of a breakthrough and Sharp swivelled in the box and drew a decent tip-over save from Cahill. But the outcome, if at all in doubt anyway, was made concrete when Ballard completed his hat-trick as he fired in Connolly's centre from a few yards out.
Here's how we rated the players at Brisbane Road:
13. Brandon Hanlan 4
Put himself about but yet another game with no real end product or attempt at goal Photo: Howard Roe/AHPIX LTD
14. Robbie Gotts 5
Buzzed about when he came on and added some much-needed energy Photo: Howard Roe/AHPIX LTD
15. George Broadbent 5
Hard ask to make things happen, especially with the game going how it was when he was introduced. Photo: Howard Roe/ahpix.com