The striker netted either side of half-time to put Colin Calderwood's side into a 2-0 lead, before Kris Commons struck a fine solo goal to put Forest in command.
A late strike from substitute teenager Matt Thornhill only added to Orient's misery.
It was Forest's 11th home game unbeaten in League One and a victory that has left them hot on the heels of leaders Swansea City.
It was actually Orient who made the more positive start to the match and who will have felt unfortunate not to have taken the lead after dominating the opening 25 minutes.
The man at the centre of it all was playmaker Sean Thornton, who had Forest chasing shadows.
In the fourth minute the former Sunderland man sent a curling shot floating wide of the post.
Two minutes later he forced the first of two outstanding saves from Paul Smith after sending a free-kick arrowing towards the top corner of the net until the keeper stretched to palm over.
Forest had a half-chance when Lewis McGugan fed a quick free-kick to Commons in the box, but keeper Stuart Nelson made himself big to block the winger's shot.
But it was Thornton who was soon having an influence again, this time as he fed Andy Barcham through the middle with an incisive pass that split the Forest defence with Smith denying the Orient man with a brave save at his feet.
Thornton came even closer to breaking the deadlock in the 24th minute when, having found himself in space 25 yards out, he launched a vicious shot that thudded back off the post and away to safety.
But Forest then sprang into life in emphatic fashion and, when Commons curled a corner temptingly towards the far post, Grant Holt arrived to crash home a header firmly into the back of the net.
It was then the home side who finished the first half in the ascendancy with Clingan firing a low shot powerfully into the side-netting and Arron Davies forcing a spectacular reaction stop from Nelson with an instant shot on the turn.
Wayne Gray was denied an equaliser for Orient after the break as Smith produced another top-notch save at the striker's feet.
And Forest soon doubled their advantage following a moment of recklessness from Orient keeper Nelson.
After Holt had been sent clear by McGugan, the keeper hauled the striker down as he burst into the box and, after referee Williamson had pointed to the spot, Nelson was relieved to escape with only a yellow card.
However, Holt completed the punishment as he got to his feet to lash the penalty low into the bottom right corner of the net.
With Orient's spirit broken, Commons added a third with a fine individual strike that saw him elude two challenges on the right flank before switching the ball onto his left foot as he burst into the box to fire a rasping shot in off the foot of the far post.
And Thornhill completed the rout in the final minutes with a scrambled close-range finish after being set-up by fellow sub Emile Sinclair.