The visitors started with a breakthrough as Justin Miller prodded the ball through for Gary Alexander to break through the rearguard and slot the ball home with Wrexham defenders waiting for an offside flag that stayed down.
Orient should have had another goal when Matt Lockwood crossed and Jabo Ibehre failed to get direction into his header as he made contact six yards out.
Again when Shane Tudor was through on the right, a strong challenge by Danny Williams saved the home side as he turned the ball for a corner.
Orient were through once more when Tudor crossed and Ibehre turned it back to Alexander to hook a shot towards the top corner, only to be denied by Michael Ingham with a one-handed tip over the bar.
A penalty two minutes before half-time put the visitors further in front when Simon Spender seemed harshly to pay the price for handball and Lockwood stepped up to beat Ingham from the spot.
Wrexham had their chances too, but failed to make the most of them. Mark Williams shot wide after Jon Walters set him up and again when Mark Jones was unmarked his shot went high over the bar.
Jones shot wide from another chance and Danny Williams missed from long range.
Dean Bennett nearly set Wrexham up for a goal on the hour, crossing for Walters to try a header that Glyn Garner kept out with a flying save.
The Orient keeper was on form again as he kept out a shot from Mark Jones, diving to save at the foot of a post.
With ten minutes to go Wrexham had a lifeline when Gary Alexander was penalized for a foul on Danny Williams, but Bennett's spot-kick was too tame, giving Garner an easy save as dived left to hold it on the ground.
With time running out Bennett made amends, getting a late consolation as the ball rolled over the line when earlier shots from Mark Jones and Marc Williams failed to beat Garner in a goalmouth scramble.