A goal from Tyrone Barnett, just minutes after the striker had been introduced as a half-time sub, secured another crucial win for Micky Mellon's side.
In a game where they were far from their free-flowing best, Town's defence withstood heavy pressure in the second-half but held on to record their 24th clean sheet of the season.
Despite having two games in four days over the Easter break, boss Mellon decided to keep faith with the team that secured the 2-0 win over Dagenham & Redbridge on Good Friday.
It meant Town lined up in their preferred 3-5-2 system, with skipper Liam Lawrence starting in central midfield against the club who handed him his professional debut 16 years ago.
Full of confidence following four straight victories, Shrewsbury came flying out of the traps and almost opened the scoring inside the first two minutes.
A free-kick from the left made its way across the box and to the back post, where Connor Goldson took a touch before smashing a half-volley across the face of goal.
The early stages were proving to be fairly even with Mansfield passing the ball around well but with Shrewsbury having the greater attacking threat.
And the away side's positivity was almost rewarded when goalkeeper Lenny Pidgeley dallied following a long ball over the top.
The goalkeeper then had to produce a Cryuff-like turn to escape the striker's attentions.
Determined to get a foothold on the game, Mansfield worked their first clear opening mid-way through the first-half.
A long punt forward saw Jack Thomas race clear, but the midfielder fired over under pressure from Jermaine Grandison.
Buoyed by the move, the Stags started to pile forward with Thomas seeing a low strike from the edge of the box blocked by Goldson.
Salop supporters began a round of applause in the 35th minute in an emotional tribute to late Shrewsbury fan Nick Mann.
And Town's players responded on the pitch by regaining the initiative and forcing a number of free-kicks around the Mansfield box.
However, the first-half petered to a close with neither goalkeeper having been truly tested following an evenly contested 45 minutes.
Clearly unhappy with his charges, Mellon made his first substitution at the break and switched Jean-Louis Akpa Akpro for Tyrone Barnett.
And the change proved to be an inspired one with the former Peterborough striker breaking the deadlock just five minutes later.
A Mark Ellis cross from the right took a huge deflection and looped up and over Pidgeley with Barnett on hand to bundle the ball home from close range.
After referee Tim Robinson was forced to make way through injury, Mansfield boss Adam Murray made his first change – swapping Terry Hawkridge for Matt Rhead.
The move saw the Stags switch from a 4-1-4-1 formation to a 4-3-3 with the change looking to be a positive one with the home fans calling for a penalty minutes later.
A cross into the box saw Jermaine Grandison mistime a header with the defender then out muscling Vadaine Oliver who took a tumble in the box.
But with the home supporters roaring for their first spot kick since November 2013, the new referee waved away the protests much to the anger of everyone on the Stags bench.
In glorious sunshine, the momentum was now with the home side and they should have equalised when some neat build-up play saw the ball worked to Chris Clements in the box, but he screwed his shot wide.
Mellon responded by introducing Andy Mangan for Collins with 15 minutes left to play.
But it was the home side who were continuing to press, with both Ryan Woods and Goldson picking up yellow cards in quick succession as they looked to stop the Stags from coming forward.
And, with five minutes remaining, Mansfield were presented with a glorious chance to get back on level terms.
A Rhead flick sat up perfectly for fellow substitute Rakish Bingham who had found himself in space after getting in-between Town's centre-backs.
But despite having time to steady himself, the striker could only scuff a shot at goal from 12-yards which was comfortably claimed by Jayson Leutwiler.
Town were now having to withstand heavy pressure as the fourth-official indicated eight minutes of stoppage time.
But despite enjoying the lion's share of possession, Mansfield were unable to truly test Leutwiler and Town held on for a vital three points and a 24th clean sheet of the season.

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