Goalkeeper Tom Collins also tipped a late penalty onto the post to keep the clean sheet in tact as United head into the next round, where the reward is a trip to Southend United in the next round.
The first attack saw Charlie Barks play a ball through to Reon Potts, but the away goalkeeper ran out quickly to gather before the Iron striker could get there.
Potts, McAtee and George Hornshaw then linked up before the ball was played to Colclough on the right, whose run into the box was halted by a defender and the goalkeeper managed to save his deflected effort.
The Iron soon won a corner on the right, and Clayton Lewis played it to Colclough, who drove into a central position outside the 18-yard-box but fired wide.
With seven minutes gone, Lewis curled a free-kick from the right into the area, but the ball just evaded McAtee and it went out for a goal kick. Soon after, Potts sent a speculative ball in from the left flank that went out for a goal kick too.
The Shrews then attacked down the left through Jamaine Turner but Finley Shrimpton defended well to see him and the ball off the pitch and win a goal kick.
There was then a great turn from Colclough after Hornshaw’s throw-in from the right, as he advanced into the area and went down but claims for a penalty were denied.
The 17th minute saw a great block from Hornshaw as Turner looked to send a cross in, and then a further challenge from the No 2 saw the ball out for a corner. James Rowland sent it in but Luke Ward’s header was blocked away and cleared.
Shortly after, McAtee received the ball on the right side and drove into the area before unleashing a powerful low shot which was tipped out by the Shrews goalkeeper.
Next to send the ball into the six-yard box was Lewis, who cut inside from the right after receiving a Colclough pass, but the away goalkeeper gathered the clipped cross into the area.
The 27th minute saw an incisive attack as skipper Mason O’Malley won the ball back down the left and played it to Yasin Ben El-Mhanni, who then sent the ball to McAtee, whose perfectly weighted pass finds Colclough. The No 7 drilled a low strike across goal but just wide.
There was soon more classy attack play from McAtee, this time playing the ball to the left side of the area for El-Mhanni but his strike was blocked away.
After a ball into the box by Rowland from the left, Shrewsbury’s Archie Elmore miscued and it was cleared. McAtee then won more applause from the Iron faithful as he played a well executed ball to El-Mhanni on the left, but the Shrews got back and cleared.
The 36th minute saw a great ball to Hornshaw by Joey Dawson, as United attacked down the right. His cross met Potts, who twisted and turned but saw his strike blocked away.
McAtee then advanced down the right side and into the 18-yard box, but his near post effort was saved by Agius.
41 minutes saw a brilliant twist away from his man from Colclough on the right, following Hornshaw’s pass. He then cut inside and kept going before pulling the trigger 20 yards out and firing just over.
Before the break, Yasin Ben El-Mhanni drove down the left and shot goalwards but his effort was blocked and it then deflected out for a goal-kick.
The away side attacked down the left at the start of the second period and then sent the ball inside to Bell, who fired well over from 20 yards.
United took the lead in the 49th minute when O’Malley took a throw down the left, and McAtee then won a corner after probing down that side. Ben El-Mhanni sent the ball in and McAtee powered a header into the back of the net.
Within four minutes, the Iron had made it two as Colclough attacked down the right side following Lewis' pass and then cut inside and fired low to Agius’ left from the edge of the area and into the back of the net.
McAtee comes close again moments later, twisting on the edge of the box before firing low and hard, seeing his shot take a deflection out for a corner.
Barks cleared the ball from the edge of his area on the hour mark and it reached Potts, who wan onto it, won the ball and sent a shot just wide of the goalkeeper’s bottom left-hand post.
Two minutes later, O’Malley passed forward and out wide to McAtee on the left. He had the vision to send the ball diagonal to right-back Hornshaw, whose effort from 20 yards went just over.
With 68 minutes gone, Colclough and McAtee linked up again, with the latter reacting to the former’s clipped pass by cutting inside and sending a shot goalwards which was saved by the away goalkeeper.
Four minutes after, McAtee showed great pace, as he was sent away down the right. His cross was cleared for a corner. It was taken by Lewis and headed just over the bar by substitute Tom Pugh, who attacked the near post.
With 73 minutes gone, the away team won a corner, which was taken by Rowland. It was cleared and reached Barnett, whose low drive from the edge of the area went wide of the left-hand post of Collins, who had it covered.
Four minutes later, Pugh and Colclough combined to win the ball, with the latter’s pass finding substitute Levi Gallimore. The striker played it back to McAtee, whose shot was blocked behind for a corner, which was then cleared.
Then, Colclough took the ball down the left side of the 18-yard box and then turned to cut inside before sending a ball into the box which the Shrews goalkeeper gathered.
The away team won a penalty in the 83rd minute as as Rowland was adjudged to have been felled. Barnett stepped up, with Collins guessing the right way, diving left and tipping it, with the ball ricocheting away off the post.
The last Scunthorpe chance saw Wilson get the ball deep on the right wing and play back to Colclough, who sent a low drilled effort in but it went wide of the near post.
IRON: Collins, Hornshaw, O’Malley, Dawson (Pugh, 70), Barks, Shrimpton, Colclough, Lewis, Potts (L Gallimore, 65), McAtee (Wilson, 85), Ben El-Mhanni.
IRON SUBS NOT USED: Baker, Jessop.
SHREWSBURY: Agius, Bell, Walker, Taylor, Davies, Ward (Caton, 69), Barnett, Rowland, Elmore, Grosvenor (Redding, 45), Turner (Hartley, 57).
SHREWSBURY SUBS NOT USED: Bevan, Sears.
