They had the perfect start with two goals from loan signing Tresor Kandol in the first 13 minutes.
Kandol, signed from Leeds United, headed home in the eight minute from close range from a cross by Lewis Grabban.
Then on 13 minutes he put a right-foot shot out of the reach of keeper Danny Coyne into the corner as Gary Alexander headed on a long free-kick by keeper David Forde.
Tranmere found little going right as they missed Ian Goodison and Edrissa Sonko away on international duty. Bas Savage was unlucky to see a first-half effort deflected wide.
In the second period Lions keeper Forde saved well from Andy Taylor and Chris Shuker, while sub Gareth Edds with his first touch chipped well over when he should have done better.
It was all over for the Merseysiders in the 60th minute. They looked in vain for offside as Kandol this time turned provider to leave Nadjim Abdou an easy finish from eight yards.
David Martin and Marc Laird were excellent for the winners who had lost 0-4 at home in their previous outing.
Savage worked tirelessly for the home side, but really it was a wet afternoon to forget, even though Savage headed a consolation in injury time from a Shuker free-kick.
Chris Hackett, Tony Craig and Zak Whitbread collected cautions for the visitors, who consolidated their top-six placing with a convincing display.