Ecuador winger Jefferson Montero's first goal in English football broke the deadlock after 76 minutes before substitute Ki Sung-yueng settled matters in stoppage time with a firm sidefoot finish.
The win extends Swansea's advantage over ninth place to six points with three games of the season remaining and the Welsh club look on course for their highest-ever Premier League finish.
Stoke had started the day in ninth spot but they offered precious little in attack and were reduced to 10 men for the first time in the Premier League this season when Marc Wilson tripped Montero five minutes from the end to collect a second yellow card.
The first half was a forgettable affair but Swansea eventually found the fluency which had been missing from their game and dominated the second period.
But it looked as if they might be denied until Jonjo Shelvey kept the ball in down the right flank and crossed to the far post where Montero beat Phil Bardsley to score with a diving header.
Stoke were a man short when substitute Modou Barrow broke free and found Shelvey at the far post, the midfielder pulling the ball back for Ki to score with aplomb.
There was an edge to the early stages as if the events at the Britannia Stadium when the two sides met in October was in the minds of both sets of players.
On that occasion Swansea manager Garry Monk accused Stoke's on-loan winger Victor Moses of "cheating" to win a penalty and that raised the hackles of his Stoke counterpart Mark Hughes.
Stoke settled well and harried Swansea to such an extent that the home side were unable to find any sort of fluency.
But the first opportunity still fell to Swansea when Montero crossed to the far post and Nelson Oliveira volleyed into the side netting from an acute angle.
Stoke were unable to fashion any chances but they enjoyed a fair share of possession and did a fine job of protecting goalkeeper Jack Butland, who had replaced Asmir Begovic to make his first Premier League start since January 2014.
The game finally stirred into some sort of life in the final five minutes of the half after Charlie Adam tried his luck but was off target from 25 yards.
Swansea lost Oliveira to injury but Neil Taylor made good progress down the left to deliver a cross which saw Nathan Dyer tee Shelvey up for a shot which flew straight at Butland.
Stoke instantly replied as Steven N'Zonzi forced Lukasz Fabianski to tip over his bar and Ryan Shawcross should have done better from the resulting Adam corner when he lost his marker but headed wide.
Swansea needed to raise the tempo at the start of the second period and they were almost immediately rewarded for doing so when Marko Anautovic slipped to present Angel Rangel with possession.
Rangel squared the ball to Gylfi Sigurdsson and the Iceland international rattled the crossbar from 20 yards.
Sigurdsson had an even clearer sight of goal from Dyer's centre but he could not keep his header down and Butland waved it over the bar.
Swansea were now firmly in the ascendancy and Shelvey saw his shot blocked before Sigurdsson's follow-up was deflected wide, but Stoke were unable to hold out in the closing stages.
Source : PA
Source: PA