Zoumana Bakayogo grabbed the first for Rovers before fellow Ivorian Akpa Akpro struck twice in eight second-half minutes to hand the hosts the points - Michael Symes notching a late penalty for Orient.
After an impressive start by Tranmere, Bakayogo made no mistake from six yards after being set free by Jake Cassidy in the 34th minute.
David Mooney almost snatched an equaliser for the O's on the stroke of half-time only to see his effort drop agonisingly wide of a post.
But Akpa-Akpro pulled out an early contender for goal of the season when he doubled Rovers' lead after 57 minutes, cutting inside his man and curling a 20-yard strike into the top corner.
Akpa-Akpro grabbed his second when he met James Wallace's pin-point cross to head home, and at the other end Mathieu Baudry let fly with a shot that whistled past the upright. Symes gave them some consolation when he fired home from the penalty spot after Bakayogo had climbed all over Jimmy Smith two minutes from time.