Two second half goals from Kyle Wootton and Paddy Madden looked to have won it for the visitors, but Jean Louis Akpa Akpro snatched a point for Micky Mellon's side at the death.
There was just one alteration from the side which beat Doncaster Rovers in midweek, with Jack King coming in for the injured Stephen Dawson.
The rest kept their places, as Luke Daniels started in between the sticks and Jordan Clarke, Murray Wallace, David Mirfin and Conor Townsend made up a four man defence. The only change was that one in midfield, with King replacing Dawson to partner Jamie Ness and Neal Bishop. In attack, Jim O'Brien, Madden and Tom Hopper were in from the off once more.
Despite the visitors making a bright start to the match, it was in fact Micky Mellon's side who had the first real opportunity of the game, inside the 10th minute. There was a freakish nature to the opening too, as Daniels' kick rebounded off Mirfin, leaving Kyle Vassell one on one with the United stopper. The Shrewsbury man lacked composure however, and blazed his effort over the crossbar.
The Iron were straight back on the front foot though, with Madden breaking the offside trap in the opposing box. The Irishman was met by Shrews' goalkeeper Mark Halstead, who rushed off his line to prevent the striker from poking the ball through his legs.
Madden threatened again, five minutes later. This time the United number nine struck from distance, after receiving the ball via a flick on from King. But he was frustrated by Halstead, with him making a save low down to his right.
Twenty minutes into proceedings a goal did come but, unfortunately for the Iron, it was for the home side. It came through Sully Kaikai, who was the first to react as the ball dropped in the penalty area, before firing into the roof of the net.
United's response was a positive one and they went very close to levelling things up on the half an hour mark. Wallace picked the ball up on the left flank and sent over a dangerous cross, which got a deflection off a Shrewsbury defender. It was a deflection which probably deceived Madden, who sliced wide at the far post.
Nick Daws' side couldn't find a route back into the game before the break and went in at half-time trailing to Kaikai's strike.
The pattern of play was similar in the second half to that of the first, with the Iron trying to force an opening. O'Brien went close ten minutes after the resumption of play, turning and arrowing a shot wide from around 25 yards out.
It took 70 minutes, but finally United made the breakthrough. Madden was the first to react after a mistake in the Shrewsbury midfield and he then played the ball through to substitute Luke Williams, who had the presence of mind to square the ball for fellow substitute Wootton. Wootton still had a lot to do, under pressure from two onrushing defenders, but the 19-year-old calmly finished into the right corner of the goal.
Before the travelling Iron supporters had time to calm themselves down after Wootton's equaliser, they were celebrating again, as Madden completed the turnaround. The goal was a problem of the home side's own making, with a Shrewsbury man misplacing a backpass, which the United striker then latched onto, giving him the chance to then round Halstead and finish with consummate ease.
The five additional minutes at the end of the 90 of normal time gave Mellon's team hope of salvaging something at the death. Hearts were in mouths as the ball dropped for Vassell in the area, but he could only blast his effort over the crossbar.
United couldn't hang on though as, with seconds remaining on the clock, substitute Akpa Akpro levelled with a cross which evaded everyone and found its way in at the far post to seal a share of the spoils.
Shrewsbury Town: Halstead, Sadler, Vassell, Whalley (Akpa Akpro 71), Kaikai (Mangan 77), Grimmer, Ogogo, Knight-Percival, Clark, Cole, Smith.
Substitutes not used: Burton, Grandison, Wellens, Vernon, Grandin.
Scunthorpe United: Daniels, Clarke, Wallace, Mirfin, Townsend, King (Williams 63), Bishop, Ness, O'Brien, Madden, Hopper (Wootton 56).
Substitutes not used: Anyon, Laird, Goode, McAllister, McSheffrey.
Attendance: 5,028 (332 away).