Orient dominated the game for long periods but failed to find a way through the Yeovil rearguard.
However, it was enough to lift Orient off the bottom of the table and their improvement continues as they have lost just one of their last six league games, but the point saw Yeovil drop from second to fifth.
In an entertaining first half both sides attempted to play football and after early pressure Orient almost took the lead but no-one was able to touch home skipper John Mackie's header.
But Yeovil always looked enterprising on the break with the pace of Arron Davies giving the home side plenty to think about.
Indeed Orient goalkeeper Glyn Garner did well to push an effort from Davies around the post after it had bounced awkwardly in front of him.
Then, on 22 minutes, Davies cut in from the right and sent an effort thudding against the Orient post.
O's boss Martin Ling made an early change when teenager Jason Demetriou replaced Donny Barnard who was suffering with a hamstring problem.
As the half progressed Yeovil took a vice-like grip on midfield and Anthony Barry went close when he fired in a 25-yard drive but again Garner saved well.
The complexion of the game changed in the second half as Orient took control and should have gone on to win the game.
The lively Wayne Corden just failed to touch home Gary Alexander 's cross, although Yeovil always carried a threat on the break and Barry's effort from distance was touched over by Garner.
Orient should have taken the lead just before the hour as Jabo Ibehre failed to find a finish from six yards, then Corden blasted over following excellent work by Adam Chambers.
Corden, Shane Tudor and Chambers all went close before Yeovil almost snatched victory with two chances in stoppage time.
First Martin Cranie saw his header tipped over and then Nathan Jones fired in a dipping effort that was pushed away by Garner.