The struggling visitors rarely threatened and were lucky to escape with only a 5-0 drubbing.
Peterborough might have gone ahead in the 14th minute but home keeper John Achterberg produced a smart save to tip over a powerful header by Mark Arber.
Tranmere were ahead just two minutes later. Paul Hall capitalised on a defensive howler to collect a through ball from Iain Hume and net with an angled shot.
Hume set up Theodore Whitmore for the second in the 29th minute and then Jason McAteer made it 3-0 in first-half injury-time with a neat finish into the corner with Hume again the provider.
Tranmere continued to control after the break and Whitmore made it 4-0 on the hour with a delightful left-foot effort from Hume's cross.
Then Hall went on a solo run to make it 5-0 in the 80th minute.
It needed a smart stop by Mark Tyler to keep out a Danny Harrison effort in the 82nd minute.
Tranmere then had the luxury of a missed penalty after Chris Dagnall was impeded by Arber. Hall grabbed the ball looking for his hat-trick but his shot was superbly turned aside by the Posh keeper.
But Hall and Hume ran the show for the Merseysiders. Skipper Curtis Woodhouse tried his best for the visitors but a 12th away reverse leaves them deep in relegation trouble.