The game's decisive moment came as early as the third minute when Ashley Williams brought down Bojan and the Spaniard confidently tucked away his second goal of the season to guide Stoke to victory and 11th place.
But Swansea might wonder whether it should have played against 10 men for most of the night following goalkeeper Jack Butland's rash challenge on Andre Ayew outside the area after 17 minutes.
Butland took a bad touch from Geoff Cameron's back pass and as Ayew closed in on the ball the England goalkeeper went in to the challenge studs first.
There was no doubt that Butland took the ball but some officials might have considered his actions reckless and reached for the red card.
Referee Robert Madley, however, judged it a fair challenge and waved play on much to Swansea's obvious displeasure.
The odds appeared stacked against Stoke as it had not won at the Liberty Stadium in four previous Premier League visits and it was almost four years since the Potters managed successive wins on the road.
Bojan slipped past Federico Fernandez and tempted Williams into a careless challenge which was firmly punished from the spot, the fourth penalty in the last five fixtures between the two clubs.
Bafetimbi Gomis met Cork's cross to send a header wide but Stoke was almost the architects of its downfall when Butland's bad touch might have landed him in trouble.
Joselu's acrobatic bicycle kick drifted wide but Xherdan Shaqiri created a clearer opening when his reverse pass caught Neil Taylor sleeping and Glen Johnson flashed his shot across goal.
Swansea was struggling to find any rhythm and slick Stoke approach play between Glenn Whelan and Marko Arnautovic deserved a better finish than Charlie Adam's wasteful effort.
The pattern remained the same after the interval with Swansea labouring for an opening and Stoke lively on the counter, Shaqiri firing wide twice and Arnautovic having the ball in the net only to be flagged for offside.
But Swansea was within inches of equalising when Jonjo Shelvey raced onto Ayew's pass and fired under the body of Butland to strike the far post, the closest they got to scoring.
Substitute Gylfi Sigurdsson also went close with a long-range effort but Stoke's excellent defensive organisation kept them at bay.
For Swansea, its worrying slide continues and now falls to 14th place in the Premier League table.
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