The Swans took an early lead through Thomas Butler and then second-half strikes from Darren Pratley, Butler, Paul Anderson and Warren Feeney, in stoppage time, completed the rout.
Swansea could not have dreamt of making a better start. The game was only four minutes old when Butler picked up the ball wide on the left and drilled a shot from a tight angle past Stuart Nelson from 25 yards.
Orient responded and went in search of an equaliser as Charlie Daniels, making his first League start, fired in a shot from distance that Swansea keeper Dorus de Vries saved well.
As Orient continued to press Adam Boyd and JJ Melligan also went close to a leveller but Swansea always looked lethal on the break and Anderson's long-range shot was well-saved by Nelson.
Orient should have levelled on the stroke of half-time when Melligan found himself clean through but shot wide.
Orient have scored 15 of their 19 League goals this season in the second half but any chance of a revival was wrecked 22 seconds after the break.
Pratley found himself in space 30 yards from goal and fired in a wonder shot that rattled the bar and hit keeper Nelson before bouncing into the net.
Swansea threatened every time they pushed forward and on 52 minutes Butler added a third when he powered down the left, beat Orient skipper Stephen Purches, and slipped the ball under Nelson's body.
Five minutes later the Welsh side added a fourth when Orient defender Aiden Palmer was out-paced and the impressive Anderson then fired the ball under the Orient keeper.
The game was over as a contest and although Orient substitutes Wayne Corden and Jason Demetriou went close to pulling a goal back it was the deadly Swans who struck again in stoppage time when Feeney out-paced Alton Thelwell and rifled home a fifth.