The Republic of Ireland international met Oussama Assaidi's pinpoint cross on 76 minutes to give the Potters victory after Wilfried Bony and Charlie Adam had both scored penalties
The visitors looked like the better team in the first half and went ahead when Wilfried Bony struck from the penalty spot after being hauled to the ground by Ryan Shawcross as a corner came in.
However, Stoke were given the chance to level things up just before the break when Angel Rangel was, perhaps harshly, adjudged to have pulled back Victor Moses in the area and Charlie Adam duly found the bottom corner of the net.
|By Tom Maston
On one of the most entertaining weekends in recent Premier League history, few expected Stoke City and Swansea City to maintain the same level, but the two mid-table sides did their best to raise the excitement levels at the Britannia Stadium.
Referee Michael Oliver will undoubtedly take the headlines after awarding two disputed penalties, with his decision for Stoke's spot-kick the turning point in a game that Swansea had dominated.
It was only after the impressive Charlie Adam converted from 12 yards that the Potters looked like taking anything from the game, and though Asmir Begovic made two fine saves, they were well deserving of the three points that were secured by Jonathan Walters' header.
After a poor start, Mark Hughes' team are into the top half and looking up.
Stoke made three changes to the starting line-up used in a 3-1 loss at Sunderland before the international break, with Erik Pieters, Mame Biram Diouf and Stephen Ireland replacing Marc Muniesa, Glenn Whelan and Marko Arnautovic.
Swansea, meanwhile, were without Ashley Richards and the suspended Jonjo Shelvey, as Rangel returned from a ban and Tom Carroll, on loan from Tottenham, came in for his first Premier League start.
Gylfi Sigurdsson had a great chance to open the scoring early on when he was put through by Wayne Routledge, but the Iceland international bundled the ball out of play with a clumsy touch when trying to round Asmir Begovic.
The Stoke goalkeeper then did well to save with his legs from Ki Sung-yueng following fine build-up play by Bony and Sigurdsson.
Begovic was beaten in the 34th minute, though, when Bony sent him the wrong way with a calmly taken spot-kick after Shawcross had been penalised for dragging the Ivory Coast striker to the ground at a corner.
Referee Michael Oliver was involved at the centre of the action again when pointing to the spot two minutes before the break after Rangel gave Moses' shirt the slightest of tugs, and Adam fired low to Fabianski's right to equalise.
Adam tested the Swansea defence with a low free-kick early in the second period but clear-cut chances were proving rare.
Stoke boss Mark Hughes introduced Walters and Geoff Cameron on the hour mark in a bid to liven things up and it was the former who made the difference when nodding in a cross from another late replacement, Oussama Assaidi.
Begovic comfortably dealt with a Ki free-kick and Bony fired wide when well-placed as Swansea offered little in the way of a late response, with Stoke seeing out victory to move level on 11 points with their visitors and into the top half of the table.