Boulding struck in each half to take his tally to 15 while League Two top scorer Aaron McLean drew a blank as depleted Mansfield deservedly upset the form book at the same time as other results went their way.
Carl Muggleton made an outstanding save at 0-0 and then the whole side dug in for an excellent victory with Boulding, John McAliskey, Stephen Dawson John Mullins and Martin McIntosh in superb form.
It is now 458 minutes since Stags leaked a goal at home, though Boulding's first goal was their first League strike in 419 minutes.
Mansfield suffered a double pre-match blow when centre halves Buxton (tonsillitis) and John-Baptiste (back strain) were ruled out.
McIntosh came back in for his first start since 22nd September and he was partnered by Jelleyman with Martin back from injury at left back.
Dawson was passed fit to play after an ankle injury last weekend and McAliskey replaced Brown up front.
Hamshaw warmed Tyler's hands with a shot after only 36 seconds but it was always straight at the keeper.
League Two top scorer McLean showed why he is up there on four minutes as his first touch took him between two defenders and into space down the centre only to screw a dreadful finish wide to Mansfield's relief.
On 10 minutes Stags won a free kick 30 yards from goal which McIntosh curled tamely into Tyler's arms.
Muggleton came to Mansfield's rescue on 19 minutes after Jelleyman allowed Boyd to rob him and send Mackail-Smith in on goal, the keeper spreading himself to block the low finish.
A minute later McLean was booked for a late lunge at Muggleton as the keeper grabbed the ball ahead of him.
Muggleton was then fortunate when he spilled a McLean cross from the left by-line but D'Laryea managed to clear.
Stags wasted a good free kick situation when Boulding sent it low straight at the wall from 18 yards in the 26th minute.
Muggleton was in action again to gather a low Mackail-Smith shot.
But Boulding almost found a way through for the home side on 33 minutes as McAliskey flicked on a Martin ball and he took it on into the box and only a great last ditch challenge by Blackett prevented him forcing the ball home.
Posh broke quickly when the corner was cleared and it took a great challenge from Jelleyman on Hughes to prevent them going through on goal.
But Boulding provided the breakthrough two minutes later. McAliskey again got the flick and this time Boulding swivelled to steer a low finish just inside the right hand post.
It was Mansfield's first League goal in 419 minutes of football.
Soon after McAliskey had two great chances to extend that lead.
First he accelerated onto an Arnold pass and, with Tyler in his sights, tried to square to Boulding instead of shoot and the chance was gone.
Then he headed straight at the keeper from close range from a corner as the home fans warmed to their side's efforts.
Muggleton was again in the right place as, from a half cleared corner, Boyd hooked an acrobatic shot into the ground that flew up at the keeper.
Morgan was booked for pulling back McAliskey in first half stoppage time as Mansfield ended the first half with the slender advantage.
Hearts were in home mouths when Mackail-Smith put a dangerous ball into the home box in the opening seconds after the restart which was thankfully cleared.
But Stags kept the pressure on and Tyler had to race 20 yards out his box to beat Boulding to a lofted through ball.
However, McLean was inches wide with a header from Newton's 58th minute cross from the right.
But ace marksman Boulding snatched a crucial second goal on 61 for Mansfield.
Under pressure, an attempted Posh clearance struck Mullins and spun back towards the edge of the box where Boulding took command, kept his cool and fired a superb finish past Tyler.
Posh looked for a reply and Boyd hoisted a pass towards McLean who crashed a half volley well over from 18 yards.
It was the division's top scorer's last action as he was replaced by Howe on 69 minutes to jeers from the home fans.
Lee pulled a low shot well wide from distance and then Howe did the same from 25 yards as the home defence continued to hold firm.
Boulding almost got away for a hat-trick as he played a one-two with McAliskey and fired straight into Tyler's arms as he was forced wide.
McAliskey received warm applause as he made way for Brown with 11 minutes to go.
On 86 minutes Boyd saw Muggleton behind his low shot, but he failed to hold on to it and Mullins had to clear from the scramble as home nerves became increasingly frayed.
But they held on for a famous victory and new hope.
STAGS: Muggleton, Mullins, Jelleyman, D'Laryea, McIntosh, Hamshaw, Dawson, McAliskey (Brown 79), M. Boulding (R. Boulding 90), Martin, Arnold. Subs not used: White, Holmes, Wood.
PETERBOROUGH: Tyler, Blackett, Morgan, Newton, Hyde, McLean (Howe 69), Boyd, Keates, Mackail-Smith, Day, Hughes (Lee 62). Subs not used: Jalal, Low, Whelpdale.
REFEREE: Mark Haywood of West Yorkshire.
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