Certainly the better chances fell to the Merseysiders, but Orient kept battling away to be rewarded late on.
The home side could hardly have wished for a better start as a second minute cross by Jennison Myrie-Williams was headed down by Shane Sherriff for Calvin Zola to net his fourth goal of the season.
Moments earlier, new signing Ian Moore came close to capitalising on a poor back pass.
As Orient rallied, Jabo Ibehre chipped over from an angle and then an Adam Boyd effort after good approach work was blocked.
Charlie Daniels curled a free-kick wide and when play swept the other end, Stuart Nelson saved with his legs from Myrie-Williams.
Tranmere looked dangerous every time they moved forward with the Orient defence often at full stretch.
The busy Zola curled a 20 yarder wide of the angle and then went close with an audacious volley from the corner of the box.
Sherriff put in some good midfield work for the Merseysiders and Ian Goodison was commanding in central defence.
The visitors worked hard and Boyd tested keeper Danny Coyne with a 30-yard effort approaching the break.
Then Coyne did well to hold a close range header from Andy Barcham soon after the restart.
It signalled a good spell for the O's with Jason Demetriou and Ibehre prominent, but as the Merseysiders rallied Zola headed wide.
Goodison and Boyd both collected cautions for over-zealous challenges.
Orient rang the changes in search of an equaliser, but it was Tranmere who nearly doubled their advantage when an over-head shot by Moore brought an excellent response from Nelson.
But the visitors were not to be outdone with Adam Chambers sliding the ball under Coyne from Paul Terry's pass for an 87th minute equaliser.