Uwe Rosler's men climbed to third place with the point but will know it could have been more but for the dismissal of Jake Bidwell for a second booking after 57 minutes.
At that point the hosts were leading 2-1 after goals from Paul Hayes and Clayton Donaldson wiped out Martin Rowlands' early free-kick for Orient.
Following Bidwell's dismissal, David Mooney missed a penalty for Orient but they secured a point when Lee Cook netted in the 86th minute.
A second-half penalty from Lewis Grabban earned Bournemouth their first win in six as they triumphed 2-1 at bottom side Hartlepool.
The visitors took lead just before the half-hour when Josh McQuoid headed in firmly from close range.
Pools equalised six minutes after the break through Jack Baldwin's first career goal, but the Cherries won it in the 63rd minute when Grabban netted from the spot after Sam Collins tripped Eunan O'Kane in the area.
Enoch Showunmi's first-half strike gave Notts County a 1-0 victory over struggling Oldham at Meadow Lane.
In League Two, Clarke Carlisle hit the winner as Northampton won 2-1 at Aldershot.
Daniel Lopez fired the hosts into the lead inside two minutes, but a Chris Hackett penalty and Carlisle's 35th-minute effort gave the Cobblers the win.