Tranmere made much of the early running after Craig Mackail-Smith missed the target for Posh in the third minute.
Steve Jennings was wide from 20 yards for Tranmere but they took the lead on 16 minutes. A Gareth Edds shot was blocked but the ball fell for Charlie Barnett who beat Joe Lewis with an excellent shot into the top right corner from 15 yards.
Ian Moore found the top netting from 25 yards and then Jennings had no luck with a speculative effort on the half-hour mark.
Peterborough could not put any pressure on reserve home keeper John Achterberg. Gaby Zakuani was booked for a clumsy challenge on Bas Savage on 32 minutes and two minutes later the visitors sent on Lee Frecklington in place of Chris Whelpdale.
There was immediate improvement and top scorer Mackail-Smith levelled on 37 minutes with a shot through Achterberg's legs after an Aaron Cresswell clearance kick had struck Aaron McLean.
Mackail-Smith should have given Posh the lead in first-half stoppage time but mis-hit his close-range shot which Achterberg gratefully saved.
The home keeper saved well from McLean, Mackail-Smith and George Boyd as United made a positive start to the second period but he was lucky on 52 minutes when a Boyd effort rebounded off a post.
Russell Martin flashed a free-kick wide as the visitors kept up the momentum.
In a rare home raid Ian Moore put an angled shot a yard off target. Then keeper Joe Lewis made an excellent diving stop at the feet of Edrissa Sonko.
Tranmere thought they had taken the extra points in added time but a Savage strike was ruled out for offside.