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:
5. Jack Senior 4
One of many put through the wringer on a torrid afternoon. Did at least hack away some clearances but powerless to Orient's attacking prowess Photo: Andrew Roe/AHPIX LTD
6. Ben Close 5
Missed his header completely in the build-up to Orient's third. Didn't do too badly aside from that but nothing out of the ordinary, either. Photo: Craig Hawkhead / AHPIX LTD
7. Owen Bailey 5
Put his head in plenty but he couldn't help turn the tide. Had a chance with a header second half. Photo: Craig Hawkhead / AHPIX LTD
8. Joe Sbarra 4
A frustrating display. One moment summed it up first half when he opted to not play in Gibson who was in acres of space just ahead of him. Hooked ten minutes after half-time with his last meaningful act a good pick-out for Sharp in the box. Photo: Howard Roe/AHPIX LTD