The hosts, unbeaten at home against the Swans in this competition, fought back from the shock of falling behind in the third minute to ease the pressure on manager Mark Hughes after just one win in their previous seven outings.
Wilfried Bony's volley against his former club raised hope for Swansea, who then frustrated Stoke for the majority of the first half only to concede twice in the space of four minutes.
After Xherdan Shaqiri converted Joe Allen's throughball to level the scores, Mame Biram Diouf smashed in a left-footed shot to grab what turned out to be the deciding goal in the battle between two struggling sides.
Having failed to score throughout November, a new month resulted in a change of fortune in front of a goal for Clement's side.
Frozen out at Stoke in the second half of last season, Bony caught his former club cold with a pre-Christmas cracker. Beating Ryan Shawcross to reach Martin Olsson's early cross, he flashed a volley into the bottom-right corner of the returning Jack Butland's net.
The striker's early goal - his first for Swansea since January 1, 2015 - antagonised an already fractious home crowd. With each misplaced pass the groans grew louder and Stoke looked devoid of attacking impetus.
Yet the jeers turned to cheers when Leroy Fer - playing at the base of a diamond midfield – dawdled in possession just outside his own penalty area, allowing Allen to tee up the alert Shaqiri for his fourth of the season.
If the equaliser was unexpected, Stoke's second goal before the break may have had some of their supporters pinching themselves to check they were not dreaming.
Peter Crouch flicked on Shawcross' hopeful long ball to tee up strike partner Diouf, who capitalised on a lucky bounce off Kyle Naughton to adjust his body position and fire beyond Lukasz Fabianski.
Still, Stoke's leaky defence - only West Ham had conceded more in the top flight prior to kick-off - meant Hughes could hardly breath easy when sitting on such a narrow lead.
6 - Wilfried Bony has scored six goals in his five apps in Premier League games between Stoke and Swansea - scoring twice for Stoke and four goals for Swansea. Cool.— OptaJoe (@OptaJoe) December 2, 2017
The Welsh manager was forced into an early change in the second half when Bruno Martins Indi picked up a groin injury that, after a lengthy break in play, saw the centre-back carried from the field on a stretcher.
However, the toothless Swans still struggled to fashion an equaliser, Tammy Abraham's low cross summing up their problems as no team-mate turned up inside the area to provide the finishing touch.
The closest they came to drawing level actually came via a Stoke player, Shawcross nearly marking his 300th Premier League appearance with an own goal as only Butland's reflexes stopped his errant header from finding the net.
Diouf wasted a glorious chance to increase the advantage at the other end, failing to convert Allen's cross from the right, but his first-half strike was enough to secure three welcome points for Hughes.
Key Opta stats:
- Stoke have scored in all seven of their home Premier League games against the Swans – against no other club do they have a better 100% record at the Bet365 Stadium (7/7).
- Swansea bagged their first Premier League goal after 431 minutes thanks to Wilfried Bony.
- Xherdan Shaqiri has been directly involved in nine goals in his last 11 Premier League games (4 goals, 5 assists) – his joint-best return in a PL season.
- Wilfried Bony has scored six goals in his five appearances in Premier League games between Stoke and Swansea - scoring twice for Stoke and four goals for Swansea.