The defender struck in the second minute of stoppage time to earn a 2-2 draw and break the hosts' hearts in Shropshire.
Greg Docherty and Luke Waterfall had put Shrewsbury in control with 19 minutes left, but Raul Jimenez pulled a goal back before Doherty saved Wolves' blushes against their Sky Bet League One hosts.
Shrewsbury almost made a mockery of the 54 places between the sides but were forced to settle for a fourth round replay at Molineux.
The visitors, eighth in the Premier League, were poor, with Adama Traore wasteful and Helder Costa seeing a header well saved by Steve Arnold.
It was nearly Shrewsbury's first win over a top flight side since beating Everton in 2003 but it threatened to turn nasty after rival fans threw missiles at each other following Waterfall's goal.
Shrewsbury boss Sam Ricketts, a former Wolves captain, promised his side would be ready to scrap it out and the hosts refused to give any early ground.
Doherty, one of six Wolves changes, sliced wildly over after four minutes but it was a rare opening.
Traore's pace troubled the Shrews but he again lacked the killer touch as he demonstrated after 25 minutes.
Doherty's neat footwork saw him wriggle free on the byline and he cut back for Traore to balloon over the bar from 12 yards.
The £18million man has scored just once and is yet to register an assist, and defender Doherty was more of a danger but saw Steve Arnold save his strike – Wolves' first shot on target – after 35 minutes.
Shrewsbury were missing the necessary quality to really hurt Wolves in the first half but John Ruddy did parry Docherty's swerving effort.
It proved to be a warning shot, though, as the on-loan Rangers midfielder opened the scoring two minutes after the break.
Ruben Neves failed to halt Fejiri Okenabirhie's strong run and the midfielder slipped the ball through to Docherty, whose powerful angled drive from 10 yards flew past Ruddy into the top corner.
Stunned, Wolves tried to respond and Neves' effort deflected inches wide after hitting Ollie Norburn.
Goalkeeper Arnold then came to Shrewsbury's rescue when his excellent save kept out Costa's six-yard header.
Wolves had woken up and Arnold gathered Leander Dendoncker's low effort after 56 minutes.
But the hosts held firm and regained their composure to double their lead with 19 minutes remaining.
They won a corner and, when Norburn swung it in, Waterfall – part of the Lincoln side who made the quarter-finals in 2017 – powered in a header from six yards.
The New Meadow erupted and opposing fans appeared to exchange missiles as tempers flared between supporters.
But substitute Jimenez pulled a goal back when he converted Traore's centre from close range with 15 minutes left.
It set up a grandstand finale and Doherty levelled in the second minute of stoppage time when he nodded in Traore's cross.
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