In the 73rd minute Ryan Semple burst clear to reach Danny Crow's clever flick but keeper Kevin Pressman blocked his fierce drive and then as the loose ball threatened to trickle over the line the veteran keeper reacted the quickest to clear the danger.
Five minutes from time with Mansfield appealing for a foul, substitute Trevor Benjamin completely mis-cued with just the keeper to beat.
Two minutes later fellow sub Andre Boucaud, who had only been on for 20 seconds, headed Jamie Day's cross wide from six yards.
Despite their late pressure Peterborough almost then lost the game four minutes into stoppage time when Mansfield substitute Adam Birchall blazed over a partially cleared corner from 10 yards.
The Stags had created game's first chance from a well-worked short corner, Richie Barker heading over Gus Uhlenbeek deep cross.
A minute later Uhlenbeek was again the provider this time chipping a neat cross to the far post where Adam Rundle's header was blocked in a crowded six yard box.
In the 20th minute the visitors should have scored however, after a poor clearance from Alex Baptiste fell straight to Semple.
The striker's fierce 12-yard drive was helped goalwards by Calum Willock, but from point-blank range Jake Buxton cleared off the line and then reacted well to deny Day from the follow up.
At the other end Giles Coke's mazy run past three defenders ended with a low drive that went just wide.
Another Baptiste error almost gifted Posh the lead just before half time. The defender's poor pass was seized upon by Crow but the strikers pile driver was acrobatically saved onto the post by the flying Pressman.
Against the run of play loan striker Allan Russell almost grabbed his first Mansfield goal but his neat deflection on the end of a Rundle cross flew narrowly wide.