A late first half header from Matthew Pennington condemned Wednesday to a narrow defeat at Montgomery Waters Meadow.
The Owls rallied after the interval and dominated play but could not break through a resolute rearguard and left Shropshire with nothing to show for their toils.
Time and again Wednesday asked the question, forcing the Shrews to dig deep, which they duly did to extend their impressive home pedigree.
The contest took a while to spark and it was midway through the opening period until the first real sight of goal for either side when Liam Palmer got a crucial block on a close range effort from Ryan Bowman.
The Owls then suffered yet another injury blow when Callum Paterson was forced off after an earlier tussle with Luke Leahy and moments later Nathaniel Ogbeta headed a decent opportunity into the grateful arms of Bailey Peacock-Farrell.
Wednesday responded with Lewis Wing letting fly with a fierce drive from 30 yards that Marko Marosi gathered at the second attempt.
The game was ambling towards the break with little incident, before the hosts got the decisive goal in added time. Leahy delivered an inviting corner from the right and Pennington climbed high to steer his header high into the roof of the net.
Peacock-Farrell smothered an Elliot Bennett hit straight after the restart before Shrewsbury missed a gilt-edged chance on 53 minutes. Rekiel Pyke got to the byline and pulled back for Bowman who blazed over the bar with the goal gaping.
Fisayo Dele-Bashiru came on from the bench and had an immediate impact as Marosi dived to parry the midfielder’s low shot to safety.
The Owls were on top as the second half progressed and carved two quickfire openings that almost penetrated the Shrews’ backline.
Wing again brought the best out of Marosi with a curling drive that the keeper acrobatically tipped over and Barry Bannan’s goalbound drive was deflected inches wide from the resulting corner.
Saido Berahino fired straight down the throat of Marosi as the Owls turned the screw but the home side threatened on the counter and George Nurse missed the target after a scramble in the six-yard box.
Back came Wednesday, Marosi saved from Theo Corbeanu, and it was one-way traffic with the clock ticking down.
The Shrews dropped deep into their own half but still the Owls needed Peacock-Farrell to thwart Bowman on the counter in the last minute.
Try as they might, Wednesday just fell short of fashioning a leveller their industry merited and Shrewsbury hung on to conclude a frustrating afternoon for Darren Moore’s men.
Wednsesday: Peacock-Farrell, Palmer, Hutchinson, Johnson (Mendez-Laing 65), Paterson (Brennan 29), Wing, Bannan, Adeniran (Dele-Bashiru 57), Corbeanu, Berahino, Gregory