Conference side Wrexham rose to the challenge of taking on a team 96 places above them and looked to be heading for victory when they opened the scoring in the 73rd minute on Sunday.
Mark Carrington's header had the 4,382 visiting fans that made the journey from north Wales to Staffordshire dreaming of a shock triumph.
However, Premier League Stoke - FA Cup finalists in 2011 - eventually found their stride and secured progression to round four with a trio of late goals.
Marko Arnautovic equalised in the 80th minute, the Austrian's close-range effort allowed to stand despite a suggestion of offside.
Ireland then broke Wrexham hearts two minutes from time with a second Stoke goal, before ensuring a flattering scoreline for the hosts with another strike in injury time.
Stoke unsurprisingly dictated possession against a side four tiers below them in the English football pyramid, yet chances were few and far between in the opening stages.
Robert Huth forced Wrexham goalkeeper Jon Flatt to tip wide with a header from a corner in the 11th minute, but Stoke generally laboured in their efforts to break down the visiting defence.
However, the hosts were almost gifted the lead in the 24th minute due to a miscommunication between Flatt and Blaine Hudson.
Centre-back Hudson headed towards his own goal as Flatt decided to charge from his line, with Wrexham just managing to scramble clear to prevent an embarrassing opener.
Flatt continued to look shaky and was again fortunate not to concede in the 44th minute, the Wolves loanee grateful to see the ball roll wide of the post after kicking fresh air when attempting to clear a backpass from one of his defenders.
Wrexham could be pleased with their first-half display, but they were even more impressive after the break and went close to scoring in the 60th minute.
Striker Wes York crashed a fantastic 25-yard effort against the woodwork just moments after midfielder Johnny Hunt had seen an appeal for a penalty waved away by referee Simon Hooper.
Those near-misses appeared to spark Stoke - who threw on former Wrexham man Jon Walters - into life, Ryan Shawcross heading narrowly wide of the far post from a corner.
Flatt then atoned for his earlier struggles by brilliantly tipping a header from Peter Crouch - another replacement - over the bar.
Hughes' men appeared to be gaining a measure of control, yet Wrexham were finally rewarded for their magnificent display when Carrington struck.
The midfielder met Connor Jennings' right-wing cross with a superb header into the bottom-left corner, sending the travelling masses into raptures.
Yet the lead lasted all of seven minutes, Arnautovic restoring parity on the rebound after Crouch - who looked to be offside from Ireland's cross-cum-shot - had been denied by Flatt.
Ireland then completed the turnaround as his half-volley from the edge of the area sneaked under the outstretched hand of Flatt.
And the midfielder added gloss to the scoreline in the fourth minute of injury time, when Wrexham's keeper was unable to keep out a shot across the face of goal.
