Shrews striker Michael Symes was sent off after a 42nd minute clash with Alex John-Baptiste, but the visitors survived a second-half onslaught with keeper Chris Mackenzie the hero with two late flying saves.
The Stags, beaten just twice in six games since Billy Dearden returned for his second managerial spell at Mansfield, created a hatful of chances throughout - but Shrewsbury's five-man midfield stifled the home side's attacking wing play which had torn Torquay apart just four days earlier in a five-goal thrashing.
Mansfield almost made a spectacular start, wingman Simon Brown spotting Mackenzie off his line from 50 yards but his lob went just wide. Brown then tested the keeper with a 25-yard shot which forced Mackenzie into a save above his head.
With the home side dominating a scrappy opening, Stephen Dawson surged forward and put in the busy Brown for a first-time low cross which Mackenzie bravely saved at the feet of the sliding Martin Gritton.
Then Michael Boulding raced clear, brushed off the challenge of Marc Tierney and fired over an empty net from an acute angle with Mackenzie beaten.
Mansfield were made to pay for wasting the hatful of early chances when the visitors scored from their first attack.
David Edwards collected the ball just across the halfway line and his incisive pass allowed former Stags' striker Derek Asamoah to race clear and shoot accurately into the bottom corner from 20 yards.
The Stags were quickly back on the attack and another clever pass from Dawson allowed Boulding to cross into the area but Gritton mis-kicked with the goal at his mercy.
Then Brown's raking pass released Boulding, who shot across the face of goal and narrowly wide from an acute angle.
The home side came even closer to an equaliser on the half hour, with Tierney clearing Johnny Mullins' header off the line from a fine Matt Hamshaw free kick.
In a rare Shrewsbury counter attack, Symes turned cleverly and fired over from 20 yards.
Moments later the game boiled over with his 42nd minute red card. The striker pushed his hand into Alex John-Baptiste's face, prompting a fierce challenge for the loose ball from the Mansfield defender. The two players then clashed again and Symes was red carded for his push, while John-Baptiste was just booked.
Shrewsbury re-organised for the second half, sacrificing one of their five-man midfielders to keep a two-man attack with substitute Andy Cooke replacing debutant Lee Canoville.
As tempers flared again, Dawson was lucky to escape a booking for a late challenge on Tierney, before eventually being yellow carded for pulling back Asamoah as the striker threatened to add a second goal.
But Mansfield's pressure was eventually rewarded in the 60th minute with Hamshaw curling an inviting cross from the bye-line and Brown heading in from six yards.
Two minutes later with the home side dominating, Gritton flashed a header into the side netting after a fine right-wing attack involving Brown, Dawson and Boulding.
As the Stags piled on the pressure in search of a winner, another excellent Hamshaw cross was glanced wide from point-blank range by Boulding.
Mansfield did have the ball in the net in the 75th minute, but Gritton's header from a clever Dawson lob was ruled out for offside.
Shrewsbury almost regained the lead a minute later, but Tierney's deflected fierce drive was tipped over by the flying Jason White.
Then in a thrilling finale as the home side piled on even more pressure, Brown's delicate chip was acrobatically tipped over by the back pedalling Mackenzie, who then dived spectacularly to tip away Jonathon D'Lareya's long range pile driver.