In what will go down as a special night in the club’s history, Sam Ricketts’ men sent 1,600 travelling Salopians potty in the Potteries as, two down with 20 minutes to go, they somehow turned it around.
Boyhood Stoke fan James Bolton, a Fejiri Okenabirhie penalty and Josh Laurent’s stunning winner sealed a fourth round tie with Wolves.
It was an ‘I was there moment’ for the fans, who saw all three goals at their end to ruin Nathan Jones’ first Stoke home game.
Stoke forward Tyrese Campbell punished Town, who were poor in the first period.
However this Cup run ends, this cold night in Staffordshire will be remembered for an awfully long time.
The venue may have been half empty, but it brought back extremely fond memories of a baking hot day in May 2004, where Salop secured one of the most crucial results in their history.
Aldershot missed out on promotion to League Two that day by the virtue of spot-kick, as Scott Howie wrote himself into blue and amber folklore.
That resumed Town’s status as a Football League club, where they have since remained. While this visit to the Potteries, 15 years on, was about embarking on a memorable Cup run.
Progression would be Shrewsbury reaching the fourth round stage for just the fourth time in the last three decades.
Boss Ricketts went slightly more adventurous than the 4-5-1 formation that has suited Shrewsbury in recent games at Sunderland just after Christmas and in the first tie against the Potters earlier this month.
In came Alex Gilliead, to play on one flank, with top scorer Fejiri Okenabirhie - who was suspended for the first tie - on the opposite side.
Okenabirhie, Gilliead and Greg Docherty were behind Aaron Amadi-Holloway in an attack-minded 4-2-3-1.
Ollie Norburn was suspended for Shrewsbury, who named 16-year-old academy goalkeeper Sam Agius on the bench, with midfielder James Rowland, just turned 17.
What was lacking in attendance was made up for in voice from a vibrant, boisterous away end.
But Stoke were in the mood to catch the eye of Jones early on, lively attackers Tom Ince and Tyrese Campbell in particularly were causing problems with their searing pace.
The hosts thought they were ahead after just 10 minutes but a Peter Crouch header from Charlie Adams’ delivery, which hit the post and Steve Arnold before dropping over the line, was ruled out for offside.
To their credit the visitors were not playing to stifle, they were picking the ball up in areas looking to hurt Stoke, but could not find the required quality.
Salop left-back Ryan Haynes was again catching the eye. His cross with his weaker right foot was a few inches away from the diving head of Amadi-Holloway as Town found their feet.
But, barely 30 seconds later, the hosts led. Ince confidently burst through the Town midfield and his through ball caused chaos in the heart of Shrews’ defence. Luke Waterfall and Mat Sadler got their legs tangled and in went Campbell, 19, to finish expertly under Arnold.
That goal meant an uphill task for Town, who looked low on confidence. The visitors were going through the gears and looking threatening on every occasion as Shrews went through the motions.
Docherty and Okenabirhie, among other, were busy working, but in the opposite direction tracking their runners backwards.
James Bolton’s looping acrobatic volley was catching practice for Adam Federici and Stoke were able to double the lead nine minutes before the break.
Waterfall’s clearing header from a short corner didn’t clear Town’s lines and Campbell volleyed home from the penalty spot.
Boos from the away end marked the half-time whistle as Ricketts’ men faced a long night.
The boss made a change at the back, bringing on Omar Beckles for the ineffective Amadi-Holloway as Town deployed three centre-halves and wing-backs to stem the tide.
The new shape appeared to work with Shrewsbury looking more solid. Okenabirhie sent their first clear chance, from a Josh Laurent through ball, into the side netting.
Shrewsbury fans were superb after the break and didn’t stop. Their side responded. Okenabirhie’s blushes were spared by the offside flag after he placed a header wide from five yards.
It was all Town on the hour. The visitors were more compact and their tails were up. Gilliead fired low and wide from the edge of the box.
Shrewsbury made their second half pressure pay - and in some style.
Bolton, from Stone, who used to follow Stoke home and away, turned away in frenetic joy after rocketing a strike from the right corner of the Potters box into the opposite top corner, pinged in off the angle. A rocket.
Town were right in it with the away end firing them forward with decibel levels off the scale.
Forward they came again with their hosts shell-shocked. Laurent was played in down the left side of the box and was chopped down by Moritz Bauer right on the line.
Up stepped Okenabirhie to hammer down the middle. His first goal in six games, in front of the delirious away end.
After an uninspiring first half Shrewsbury were somehow level. And worthy of it. And they weren’t done.
As Stoke pushed, with the locals angry, they left gaps. Grant, Okenabirhie and Docherty combined marvelously on the right and the latter squared on a plate for Laurent.
He applied the touch and the 10 minute turnaround was complete. A stunning performance and result in this football club’s history.
Stoke City (4-4-2 diamond)
Federici; Bauer, Williams, Martins Indi ©, Tymon; Ince, Etebo, Adam, Clucas, Campbell (McClean, 73); Crouch.
Subs not used: Haugaard (gk), Afobe, Berahino, Edwards, Souttar, Woods.
Shrewsbury Town (4-5-1):
Arnold; Bolton, Waterfall, Sadler ©, Haynes; Gilliead (Angol, 89), Docherty, Grant, Laurent, Okenabirhie (Eisa, 88); Amadi-Holloway (Beckles, 45).
Subs not used: Agius (gk), Emmanuel, Sears, Rowland.
Referee: Geoff Eltringham
Attendance: 10,261 (1,656 Shrewsbury fans)