The home side came closest to breaking the deadlock, but Millwall's Paul Robinson made a stunning goal-line clearance to earn the visitors a precious point in their promotion push.
In a frenetic game it was high-riding Millwall that were quickest out of the blocks and veteran striker Neil Harris had two early chances, but he put the first over the bar and the second in to the hands of Orient keeper Glenn Morris.
With David Martin causing Orient problems down the left, Millwall continued to dominate the early stages, but gradually the O's battled their way back and started to cause the visiting defence plenty of headaches.
Orient striker Sam Parkin rolled a shot just wide after some good approach play before Millwall were forced into a reshuffle when Chris Hackett replaced the injured Marcus Bignot on 24 minutes.
The best chance of the first half came on the half-hour mark, when Orient's top scorer Adam Boyd latched on to Sean Thornton's flick and smashed the ball goalwards, only to see Robinson somehow scramble the ball off the line with keeper David Forde beaten.
Boyd then shot wide and Thornton had an effort blocked as Orient continued to press.
After the break Orient continued to dominate but struggled to create too many clear-cut opportunities.
The hugely impressive Jason Demetriou went close with a shot on 58 minutes, but it flew just wide, and it was the visitors who could have grabbed the points on the break.
First, skipper Robinson hit the post with a header 15 minutes from time and then the pacy Lewis Grabban powered clear of the home defence but fired wide of the target.