In a dismal first half, Orient's only worthwhile effort on goal came from Dean Morgan, making his first start, when he rifled a shot from 25 yards over the bar.
For the rest of the half it was Rovers who looked more likely to score and, on 20 minutes, a shot from visiting skipper Antony Kay from the edge of the area was well saved by Glenn Morris in the home goal.
Steve Jennings then wasted a good chance for the visitors, firing wide from 12 yards after Bas Savage set up the opening.
It came as no surprise when Tranmere took the lead just before the break.
Orient's Adam Chambers saw his attempted clearance hit team-mate Paul Terry and bounce into the path of Shuker, who shot into the right-hand corner from 20 yards.
Ryan Shotton headed just wide shortly afterwards as the visitors almost doubled their advantage just before the break.
In the second half Orient finally came to life and Jason Demetriou saw his cross from the right cannon off the far post with visiting keeper Danny Coyne beaten. Ryan Jarvis could not force the rebound home as Rovers defender Ben Chorley blocked his effort.
Orient's top scorer Adam Boyd then blasted wide from four yards following Morgan's fierce cross from the left.
In a final flourish Orient substitute Simon Dawkins was denied by the impressive Coyne after a flowing move.
With Tranmere on the ropes, Chambers headed over and Demetriou saw a free-kick saved by Coyne.
Then the visiting keeper pulled off a stunning save to deny Dawkins two minutes from time, but it was too little too late to save the home side.