The Swans fought back from 2-0 down to lead 3-2 only to be pegged back by a controversial penalty decision which sub Charlie Adam slotted home in added on time to earn Stoke a share of the spoils.
In a thrilling six-goal encounter, the Potters took an eighth-minute lead through Jonathan Walters before Stephen Ireland doubled their lead before the half-hour.
It left the Swans a mountain to climb after the break, but Wilfried Bony pulled one back with a powerful header before the hour to give the Swans hope.
Sub Nathan Dyer then fired the Swans level with quarter of an hour left to set up a grandstand finish.
And when Bony slotted home from six yards to edge the Swans ahead in the 86th minute, it looked like the hosts had completed the most dramatic of comebacks.
But the drama didn't end there.
With five minutes of added on time to come, referee Robert Madley awarded Stoke a controversial penalty after he adjudged Wayne Routledge to have handled Robert Huth's header.
Up stepped sub Charlie Adam, and the Scottish midfielder sent Gerhard Tremmel the wrong way to pinch a point for the Potters as the Swans were pegged back in the last minute for the second time in a week following on from the Europa League draw with Kuban Krasnodar.
This point moved the Swans up to 13th place and onto 12 points from 11 games.
Michael Laudrup made five changes to his starting XI.
With Michel Vorm suspended, Gerhard Tremmel made his first league appearance of the season while 18-year-old Slovenian Gregor Zabret provided the back-up on the bench in what was his first inclusion in the matchday squad.
Angel Rangel and Chico Flores returned to defence after being on the bench for the Europa League draw against Kuban Krasnodar in Russia while Leon Britton was back in midfield.
Wayne Routledge came back into the team in place of Nathan Dyer, who moved to the bench, while Roland Lamah - who made his Swans debut against Stoke last season - made his first appearance in the league this campaign.
Garry Monk, Pablo Hernandez and Michu all missed out on selection due to injury.
SWANS: Gerhard Tremmel, Angel Rangel, Chico Flores, Ashley Williams (capt), Ben Davies, Leon Britton, Jonathan de Guzman (Jonjo Shelvey, 71), Alejandro Pozuelo (Jose Canas, 90), Wayne Routledge, Roland Lamah (Nathan Dyer, 55), Wilfried Bony.
SUBS: Gregor Zabret, Jordi Amat, Neil Taylor, Alvaro Vazquez.
STOKE:Asmir Begovic, Geoff Cameron, Ryan Shawcross (capt), Robert Huth, Erik Pieters, Jonathan Walters, Steven Nzonzi, Stephen Ireland (Marc Wilson, 71), Wilson Palacios (Charlie Adam, 71), Marko Arnautovic (Matthew Etherington, 55), Peter Crouch.
SUBS:Thomas Sorensen, Glenn Whelan, Kenwyne Jones, Oussama Assaidi.
The Swans got off to a disastrous start as Stoke took the lead after just eight minutes.
With skipper Ashley Williams off the pitch having treatment for an ankle injury, the visitors took full advantage as a clearance up the pitch was nodded on by Peter Crouch for Jonathan Walters, who fended off Ben Davies and Chico Flores before firing past Gerhard Tremmel and off the inside of the far post.
The Swans went in immediate search of an equaliser and they created a good chance through Angel Rangel, whose cross met the head of Roland Lamah, but he could only direct it straight at Asmir Begovic.
While Stoke sat back on their lead, the Swans were strongly pushing for a goal, and Wilfried Bony wasted a half-chance following Wayne Routledge's cross as he could only half-volley wide.
But Stoke struck ruthlessly on a counter attack to double their lead on 25 minutes.
Scorer Walters squared to Crouch, and the England striker's first-time pass sent Stephen Ireland in on goal, and he calmly slotted past Tremmel.
The Liberty was stunned, but the Swans kept plugging away.
And they had a golden chance to pull one back as Erik Pieters' pass back dropped to Bony, but when he raced in on goal and attempted to round Begovic, the keeper got a hand on the ball to deny the striker.
Bony was at it again shortly after as he headed wide from a cross and then Chico glanced a Jonathan de Guzman corner off target before the break.
HALF-TIME: Swans 0 Stoke 2
The Swans needed a quick reaction in the second half, and they pulled a goal back in the 57th minute just shortly after introducing Nathan Dyer for Lamah.
A curling de Guzman cross met the head of Bony, and the club-record signing powerfully headed past Begovic from six yards out.
The Swans continued to push for an equaliser and were camped in the Stoke half.
Laudrup made another change as Jonjo Shelvey came on in place of de Guzman while Stoke made a double change of their own as Marc Wilson and Charlie Adam were introduced.
But it was the Swans who got the reaction they were looking for in the 74th minute as a Routledge cross was nodded out by Robert Huth to Dyer, and the substitute's half-volley spun into the net.
It was thrilling as it was tense, and it set up a grandstand finish.
The Jack Army were pushing their team on for a winner.
And the Liberty erupted in the 86th minute as sub Shelvey twisted and turned his marker inside the box before crossing low to Bony, who directed his effort low past Begovic.
Laudrup made his final change in added on time as Jose Canas came on in place of Pozuelo as the Swans looked to hold onto their lead.
And the drama continued, unfortunately for the Swans, as a re-taken corner found Huth, and his header was adjudged by referee Robert Madley to have hit the hand of Routledge.
Substitute Charlie Adam stepped up and slotted past Tremmel to earn the visitors a share of the spoils in the most dramatic of encounters.