Mansfield began Saturday afternoon knowing they could be relegated if they lost and other results went against them.
And things looked grim indeed when home keeper Jason White allowed a Marc Pugh shot to wriggle from his grasp and over the line inside the opening 75 seconds.
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But Stags stormed back to lead 2-1 at the break as Boulding finished off two Matty Hamshaw crosses.
Shrewsbury, who had only won once in 16 matches, rallied after the break and piled on the pressure on a Mansfield side that looked nervous and mentally and physically tired.
Indeed, White made amends for his early mistake with a superb reaction save on 81 minutes to deny Guy Madjo from close range.
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Boulding then finally made it safe three minutes from time on the break as he took his tally to 25 goals in an amazing season for himself in a struggling side.
With all three relegation rivals, Wrexham, Dagenham and Notts County all losing, suddenly there is hope again at Field Mill, though more nerves will doubtless be shredded in the next fortnight.
With Jake Buxton already suspended, Stags were missing two of their regular back four,
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Gareth Jelleyman failed to shake off his Achilles' tendon injury and was replaced in the side by Chris Wood.
Wood played right back with Keith Briggs switching to left back.
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But there was better news on top scorer Micky Boulding whose ankle injury had cleared up enough to start the game.
Carl Muggleton (bruised thumb) was among the subs and Dan Martin also returned to the squad.
Shrewsbury were due to be unchanged for the third successive match. But Davies dropped out of the starting line up after the warm-up and Constable was drafted in at the last minute.
Arnold had a shot charged down in the opening seconds as Mansfield began on the front foot.
But there was an almighty shock at the other end on 75 minutes as a dreadful mistake by home keeper White allowed the Shrews a sloppy goal.
Pugh's shot from 12 yards should have been kept out by White at his near post but the keeper failed to hold it and allowed it to go in.
Immediate Stags pressure saw Hamshaw crash a first time shot well over from 20 yards.
Already it was clear that things were not going Stags' way with some of the referee's decisions. Boulding was tripped but regained his feet before stumbling. An initial advantage was played but when there was none the referee played on rather than bringing it back for the free kick.
Then Tierney was lucky not to be booked for taking out Hamshaw with a high tackle. Amazingly Hibbert then caught Briggs high and late and again escaped with just a word in his ear
A great flick from Louis set Boulding away on the right on 15 minutes and he crossed hard and low back towards Louis whose close range flick at goal was blocked by Kempson.
But Stags were level on 22 minutes. Briggs' superb crossfield ball picked out Hamshaw on the right of the box. He flicked the ball brilliantly over the keeper and Boulding was lurking behind him to touch it into the empty net.
They were almost ahead four minutes later when Hamshaw sent a corner to the far post where Briggs saw his firm header saved at the foot of the near post.
The visitors worked the ball into the home box on 27 minutes but, as Constable, looked to shoot, John-Baptiste whipped the ball off his toe for a corner.
Stags broke from that and Hamshaw's long pass put Arnold into space and he cut inside before shooting straight at Bevan.
A McIntyre cross from the right saw Hibbert nod a finish wide of the far post in what was becoming a very entertaining game.
Within 60 seconds Stags were ahead on 36 minutes with Boulding's 24th goal of the season. Hamshaw crossed in low from the right to Boulding who had his back to goal with a defender up tight. But he turned sweetly to steer in a low shot from 12 yards.
John-Baptiste conceded a free kick 25 yards from goal which saw Constable fire his free kick and the follow up into the wall.
White confidently punched away two Shrewsbury corners as half time approached. And in stoppage time Hibbert tried a lob which passed well over the far angle.
Louis headed wide from a Hamshaw free kick just before the whistle brought an end to a thrilling and draining half of football.
There were worrying moments early in the second half as Mullins needed treatment in the centre circle. Thankfully he was able to continue. But Shrewsbury soon lost striker Hibbert as he was replaced by Humphrey.
Tierney again escaped a booking for a cynical trip on Louis and the Shrews cleared the free kick.
Hamshaw put another corner over which saw Briggs' volley deflect wide for another which again found Briggs but he headed tamely wide.
Mansfield were really going for that all-important third goal and Louis was only just over with a powerful dipping shot from 25 yards.
However, some scrappy defending by the Stags saw the ball break for Constable whose rushed lob was too high with White off his line.
The Shrews should have been level on 65. A Stags move broke down, the visitors poured forward and Pugh's low cross behind the home defence was controlled by Constable who, with just White to beat, flicked his finish wide of the keeper's right hand post.
With Stags looking jittery, Holland sent on the experience of Horlock for Dawson to try to calm things down.
The pressure stayed on as the visitors forced an agonising four corners. They were cleared though Majdo did force a save from White soon after as Stags continued to visibly wilt.
But Horlock and Arnold combined to send Boulding into the box and his finish was not far wide of the far post.
Pugh tried to beat White again at his near post but this time the youngster was safely behind the ball.
White atoned for his early error with the save of the match on 81 minutes. Pugh crossed low from the left and Madjo turned it on target at the near post only for White to produce a crucial reaction save.
Stags shored things up at full back on 83 as Martin replaced Wood and Briggs moved across to right back.
The home side had been under the cosh for so long, but Boulding produced the killer blow on 87 minutes. A long ball forward saw Boulding shrug off the challege of Kempson and go clear before coolly stroking home the perfect finish under Bevan to start the celebrations.
STAGS: White, Mullins, D'Laryea, Hamshaw, Dawson (Horlock 67), M. Boulding, John-Baptiste, Arnold (Brown 88), Louis, Wood (Martin 83), Briggs. Subs: Muggleton, R. Boulding.
SHREWS: Bevan, Moss, Kempson, Pugh, Hibbert (Humphrey 50), Herd, Constable (Madjo 68), Leslie (Lee 78), Murdock, Tierney, McIntyre. Subs: Garner, Ryan.
REFEREE: Grant Hegley of Hertfordshire.
ATTENDANCE: 3,334.
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