Fernando Llorente opened the scoring; Swansea’s top scorer this season was able to get free from Ryan Shawcross before meeting Gylfi Sigurdsson’s corner.
Tom Carroll then doubled Swansea's lead, his effort from a long way out deflected off Joe Allen just after Marko Arnautovic's missed penalty.
First half belonged to the home side
Swansea manager Paul Clement changed his team shape for this game, having favoured a 4-3-3 during his time at the club he decided to employ a diamond system to allow Sigurdsson more attacking freedom.
Mark Hughes himself has been prone to changing Stoke’s shape this season, but once again stuck with a 4-4-2 shape that he has been fond of in recent weeks.
However Swansea took the lead with their first chance, as Llorente towered over Shawcross to meet Sigurdsson’s corner.
Sigurdsson has now provided a league-high seven assists from set-plays this season and created 44 chances from dead-ball situations.
Swansea were the much better side in the opening exchanges, and having Leon Britton back seemed to install confidence in the side, the change in shape also offered more offensive firepower with Jordan Ayew working off Llorente.
Sigurdsson then had a chance, Swansea working off a long throw as Llorente knocked the ball down but former Swan Joe Allen was able to get in between Sigurdsson and the ball.
Saido Berahino then came close to scoring his first Stoke goal, he met Allen’s cross ahead of Federico Fernandez with his shoulder but the ball flew wide of the post.
Stoke grew more into the game, and created a couple half chances but weren’t able to force Lukasz Fabianski into a save after despite the keeper conceding 68 goals after 33 games this season.
Just before half time, substitute Ki Sung-Yeung sent Ayew into the channel. He took on Bruno Martins Indi before striking the ball was palmed away by Jack Butland, making his first appearance of the season today.
Berahino then almost tied the game up just before the whistle, getting on the end of a Xherdan Shaqiri free kick but his header was straight into the Fabianski’s grateful hands.
Second half continued in the same vein
Stoke came out strong in the second half, as Arnautovic had the first shot blocked before Peter Crouch's effort was easily saved by Fabianski.
Swansea claimed for a penalty after Ayew ran into Erik Pieters inside the box, Michael Oliver rightly waved away his pleas.
Clement then made a surprise change, as he took off goalscorer Llorente for centre-back Mike van der Hoorn as the Swans set up in a 5-3-1-1 shape.
At 6'4", van der Hoorn was probably brought on to deal with Crouch's aerial presence, but Swansea sat much deeper as a result of that change.
As they sat deeper, Stoke got closer towards the goal which resulted in a penalty as Fernandez brought down Shaqiri just in front of goal.
Arnautovic then stepped up to take the spot-kick, and went for power over precision and the end result was his effort flying way over the crossbar.
Moments later Carroll doubled Swansea's lead and sent the fans into raptures, his effort from range took a deflection off Allen and looped over Butland.
There were just 60 seconds between Arnautovic's penalty miss and Carroll's goal.
Carroll then broke free on goal and almost got his second of the afternoon, if not for a full-stretched save from Butland, who was impressive on his comeback.
Ayew then nearly got a third for Swansea, breaking free on the counter but Butland was there again to keep Stoke in the game.
The Potters haven't scored an away goal since a 3-1 win at Sunderland on 14 January.
They now have failed to score in six consecutive top-flight away matches for the first time since April 1985.
This game will give Clement's men a much-needed confidence boost, in addition to the valuable points at this stage in the season.