It was another big win for the O's, who managed to repel a late onslaught from Stockport.
Michael Raynes, Chris O'Grady and Dominic Blizzard all missed decent chances late on for the hosts.
There was a fairly pedestrian start at Edgeley Park. The first opening didn't arrive until the 12th minute and then it was a fortuitous one.
Orient defender Charlie Daniels charged down a Greg Tansey attempted clearance and the ball flew narrowly past a Stockport post.
The hosts failed to make the most of a great chance on 21 minutes. Tommy Rowe wriggled his way down the left before teeing Tansey up perfectly. However, the young County midfielder screwed a left-foot shot high and wide from 15 yards.
Still both sides huffed and puffed while producing little end product, but on 32 minutes Stockport's loan striker O'Grady tested keeper Jamie Jones with a shot from a very acute angle.
At the other end, Jason Demetriou twisted and turned before powering in a decent shot which curled inches over the crossbar.
On the stroke of half-time, Orient missed by far the best chance of the game so far.
Tamika Mkandawire headed the ball across the face of the Stockport goal, but Jordan Spence could only dive in and plant a header wide from point-blank range.
After such a dull first half, the second period began with something of a bang.
Firstly Stockport keeper Owain Fon Williams superbly denied Simon Church, then substitute Oli Johnson smashed into the side-netting at the other end.
Orient then took the lead on 52 minutes. Church crossed in from the right initially but Leon McSweeney's clearance only went back to the visiting frontman, who proceeded to fire the ball clinically past Fon Williams.
Sean Thornton went close to a second soon after when he curled a shot wide of the Stockport post.