Danny Crow was their two-goal hero but it was an excellent all-round team display which carried the day.
Tranmere looked to be in control in the opening half and led after 31 minutes, but Peterborough rocked them with an equalising goal in first-half injury time and snatched the verdict with their second strike in the 70th minute.
Tranmere suffered a major set-back before kick-off. John Mullin suffered an ankle injury in the warm-up. It meant Kevin Ellison had to be pushed into a midfield role with Craig Curran coming on to the bench.
Tranmere made a bright enough start with a Chris Greenacre header from a Chris Shuker cross turned over the bar by keeper Mark Tyler after only three minutes.
Then Shuker had a goalbound shot blocked following a Steve Davies centre.
Peterborough almost snatched the lead in the 18th minute. A Richard Butcher shot took a deflection, but was superbly turned round a post by keeper Gavin Ward.
Ward then did well to hold on to a crisp drive by Dean Holden which followed the corner.
Skipper Shane Sherriff was credited with the Tranmere goal in the 31st minute. His header from a Shuker corner struck the underside of the bar and could have got a final touch from United defender Guy Branston, before finding its way inside the far post.
Peterborough refused to lie down and Ward did hold to a shot by Jude Stirling.
Ellison was just wide for Tranmere after a Greenacre shot rebounded off a defender but then Peterborough levelled in added on time. Crow netted in style at the near post from a low cross by Adam Newton.
Tranmere in the second half got in good efforts through Ellison, Davies and Gareth Taylor without gaining any reward.
Then Ben Futcher headed wide following a Posh corner and Aaron McLean flashed a shot across the face of the goal.
The second Peterborough goal stemmed from a long throw-in by Stirling. Crow beat Ward with an excellent shot from 12 yards.
As United came again Butcher put an effort just over when set up by McLean and then Sherriff came to the rescue for Tranmere as McLean tried to work his way through.
Calvin Zola joined the action for Tranmere and almost found an equaliser in the 82nd minute. He got in a powerful header from a Davies cross, but the alert Tyler was able to tip the ball over the bar.
Posh boss Keith Alexander commented: "We played some good football and probably deserved the win. It was all about energy and commitment.
"We defended brilliantly under pressure and it was difficult to fault anyone. I am delighted."
Rovers boss Ronnie Moore moaned: "We weren't good enough on the day. We have let a lot of people down. We were not focused enough.
"Much of our play was poor. The performance was not good enough and the players know that. We should have been able to do a lot better."