Conor Chaplin gave the Blues the lead in the 22nd minute but Shaun Whalley levelled for Shrewsbury five minutes later to leave the scoreline 1-1 at half-time at Portman Road.
Chaplin replaced Bersant Celina as the number 10 in a Town side otherwise unchanged from the one which thrashed Doncaster 6-0 and was beaten 2-1 at Accrington.
Celina is currently away with Kosovo, who play Sweden in a World Cup qualifier in Stockholm at 5pm.
Shrewsbury were unchanged from the team which lost 2-1 in their last league game at Bolton last weekend. Elliott Bennett, whose father died earlier in the week, was handed the captaincy, while former Blues loanee Matthew Pennington was on the right of their back three.
Ahead of kick-off both teams took a knee to warm applause from around Portman Road.
There was an early minor scare for the Blues when keeper Vaclav Hladky kicked against Daniel Udoh but George Edmundson and then Janoi Donacien cleared the potential for danger.
Town, unusually shooting towards the Sir Bobby Robson Stand in the first half, struck the first effort of the game in the third minute, Lee Evans, a hat-trick scorer in his last game at Portman Road, curling a free-kick not too far wide of Shrews keeper Marko Marosi’s left post after skipper Sam Morsy had been fouled just outside the area to the left.
The Blues had the ball in the net in the eighth minute in a familiar fashion but with the linesman’s flag raised. Evans played in Wes Burns on the right and the Welshman crossed low for Macauley Bonne to tap home what would have been his ninth of the campaign but for the on-loan QPR man having strayed offside.
Town were dominating the early stages, moving the ball around swiftly with Shrewsbury struggling to get out of their half.
On 16 Burns headed into the side-netting at the far post from a Scott Fraser free-kick on the right - which had been delayed by jostling in the area - won after the former Fleetwood man had been fouled by George Nurse.
The game continued in the same manner and on 18 Matt Penney wasn’t too far away from his first goal at Portman Road and his second of the season when Fraser played a corner to him 25 yards out and the ex-Sheffield Wednesday man struck a powerful shot only just beyond Marosi’s left post with several of his team-mates making lunges towards it to add a final touch.
Ryan Bowman headed Shrewsbury’s first effort on goal weakly to Hladky in the 20th minute but aside from that it had been all Town and three minutes later they took the lead.
Morsy played a half-cleared ball wide to Penney, who crossed towards Bonne at the far post. Town’s top scorer headed across goal, Marosi saved but Chaplin was on hand to net his second goal in two games and his third of the season, all in his last four appearances.
But the lead lasted only five minutes. Shrewsbury started to show some attacking threat and on 28 Shaun Whalley brushed aside Morsy as they battled for a loose ball and unleashed a 25-yard left-foot shot which flew past Hladky to his right and into the net.
The Blues, in total control up until their goal, started to show nervy signs and Shrewsbury might have gone a goal up on the half hour when Udoh crossed from the left and Bowman turned over at the near post when he will feel he should have found the target.
The Shrews were forced into a change on 35 when Bowman suffered a knock with on-loan Birmingham striker Sam Cosgrove taking over.
Cameron Burgess got his name in referee Will Finnie’s book in the 39th minute for dragging back Cosgrove as the sub escaped down the right.
In the penultimate scheduled minute Shrews goalscorer Whalley scraped an effort from the edge of the box to the right well wide with the Blues ending the half scrappily.
During three minutes of injury time, the Blues finally seemed to regain some composure, passing the ball around with their earlier confidence until Bonne was flagged offside.
It had been half of two halves from Town, who had completely dominated and fully deserved their goal when it came, Chaplin continuing his recent good form in front of goal.
But from there the Blues allowed Shrewsbury, who had looked every bit a side second-bottom of the table, back into the match.
Morsy will feel he ought to have been stronger as he battled with Whalley for the ball ahead of the Shrews forward’s strike which gave Hladky no chance.
The Blues were scruffy, nervy and hesitant from there, only seeming to regain their composure in the closing moments.
Town: Hladky, Donacien, Edmundson, Burgess, Penney, Morsy (c), Evans, Burns, Chaplin, Fraser, Bonne. Subs: Holy, Nsiala, El Mizouni, Harper, Aluko, Edwards, Pigott.
Shrewsbury: Marosi, Leahy, Ebanks-Landell, Pennington, Pierre, Whalley, Udoh, Bowman (Cosgrove 35), Davis, Bennett (c), Nurse. Subs: Burgoyne, Ogbeta, Pyke, Bloxham, Caton, Lashabela. Referee: Will Finnie (Bedfordshire).