Orient were overwhelmed for much of the first half but showed tremendous improvement later and were unlucky not to get on the scoresheet.
But it was a third successive away reverse for the newly-promoted visitors who were missing key players.
Tranmere's opening goal came in the eighth minute following an offside decision against Orient. Goalkeeper Gavin Ward put the 80-yard free-kick into the visiting box, Orient keeper Glen Morris misjudged the bounce in the blustery conditions and in a desperate lunge could only help the ball into his own net.
Ironically if he had not got a touch the goal would not have counted.
Tranmere doubled their lead in the 12th minute when Chris Greenacre netted with a smart finish after a cutback from Chris Shuker.
Shuker wasted a golden opportunity to make it 3-0 when firing wide in the 17th minute. Orient nearly got back into the match in the 25th minute but Ward produced a diving save to turn a Joe Keith free-kick away for a corner.
Morris kept Rovers at bay with fine saves from Kevin Ellison and Greenacre and Ward did well early in the second half to keep out Gary Alexander's fierce effort.
Greenacre was unlucky to hit a post for Tranmere in the 66th minute from an Ellison cross but he settled the game in the 80th minute with a close-range finish after his initial header had been blocked by Morris.
Orient never threw in the towel. Shane Tudor, who worked hard in midfield, was unlucky to see a goalbound shot deflected for a corner and, in stoppage time, Alexander headed just over the bar.
Shuker produced a man of the match performance for Tranmere but there was also a five-star display from Greenacre.
Orient produced some lively play at times but paid dearly for a poor opening spell.
Greenacre picked up a first half booking for Tranmere. The Orient pair of Alexander and Brian Saah were also yellow carded in a lively encounter.