Two goals from Michael Boulding took his tally for the season to 15 - including the Stags' first goal for 419 minutes - as he outgunned the disappointing Aaron McLean.
Town, beset by injuries before the match, have now not conceded a goal at home in all competitions for 458 minutes.
Just before the kick-off they lost central defenders Jake Buxton and Alex John-Baptiste to illness and injury.
That meant full-back Gareth Jelleyman, switched from left-back to a makeshift centre-half, was joined in the back four by Martin McIntosh for his first start since September and Dan Martin for his first game in three weeks.
The reshuffled defence were up against the 32-goal strikeforce of McLean (19) and Craig Mackail-Smith (13).
And it took just four minutes for McLean to race through a static home rearguard after trickery by George Boyd, but with just Carl Muggleton to beat he dragged his shot well wide.
Then the keeper saved superbly at the feet of Mackail-Smith after a slip by Jelleyman allowed Boyd to thread a pass through the defence.
On the half-hour Muggleton again dived low to hold onto another Mackail-Smith shot. But from then on the Stags looked comfortable at the back with the recalled McIntosh outstanding.
However, the lowly home side also posed a goal threat in the opening half, Matt Hamshaw's 20-yard drive and McIntosh's free-kick both being held by Mark Tyler.
Then in the 32nd minute Mansfield carved out a fine chance, John McAliskey's flick on putting Michael Boulding clear.
The striker held off a challenge before seeing his finish half-saved by the onrushing Tyler - with Shane Blackett clearing the loose ball off the line.
But three minutes later Michael Boulding made no mistake. McAliskey was again the provider with a flick-on and this time the striker held off Blackett before turning and finding the bottom corner from the edge of the area.
The goal inspired the home side and within four minutes McAliskey had twice gone close to doubling their lead.
First he tried to find Michael Boulding in the six-yard area when it looked easier to score himself and then his close-range header from Hamshaw's corner was saved at point-blank range by Tyler.
Peterborough's players spent most of half-time on the pitch - but it was the Stags that created the first chance of the second half, Michael Boulding's deflected shot being blocked by Tyler.
The keeper then raced ten yards out of his area to clear as Michael Boulding waited to pounce on a long hopeful punt upfield.
The save almost proved vital in the 58th minute when McLean's glancing header from Adam Newton's cross flashed narrowly wide as the Posh stepped up their search for an equaliser.
And the Stags took full advantage to double their lead in the 61st minute. A clearance rebounded off Mansfield full-back John Mullins to put Michael Boulding clear of the visitors defence and he calmly tucked the ball home from 12 yards.
McLean blazed over as Peterborough increased the pressure while, at the other end, Michael Boulding had a chance to complete his hat-trick, but his powerful shot was straight at Tyler.
Five minutes from time Muggleton spilled Boyd's shot but, as substitute Rene Howe waited to pounce, Mullins cleared off the line and the Stags were off the bottom of the table.