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 send Stoke to a 1-0 victory which moves them to 11th place in the Premier League.
But Swansea might wonder whether they 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 they had not won at the Liberty Stadium in four previous Premier League visits and it was almost four years since they had managed successive wins on the road.
But Stoke were the form team of the pair, their 1-0 success at Aston Villa last time out yielding a third successive win in all competitions, while Swansea had not won in five league and cup outings.
Those contrasting confidence levels were reflected almost instantly when Jack Cork's mistake allowed Bojan to run at the heart of the Swansea defence.
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 were almost the architects of their 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 were 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 were 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, their worrying slide continues and they now fall to 14th place in the Premier League table.
TWEET OF THE MATCH
"Swansea have given the ball away more in this game than the previous 3 seasons combined."
- Gary Lineker @GaryLineker
https://twitter.com/GaryLineker/status/656206052787122176
PLAYER RATINGS
Swansea
Lukasz Fabianski 6 (out of 10)
Angel Rangel: 7
Ashley Williams: 6
Federico Fernandez: 7
Neil Taylor: 5
Jack Cork: 5
Jonjo Shelvey: 6
Jefferson Montero: 6
Modou Barrow: 5
Andre Ayew: 6
Bafetimbi Gomis: 4
Substitutes
Gylfi Sigurdsson (on for Barrow 59mins): 6
Ki Sung-yueng (on for Cork 59mins): 6
Eder (on for Ayew 80mins): 6
Stoke
Jack Butland: 6
Glen Johnson: 7
Geoff Cameron: 7
Philipp Wollscheid: 7
Erik Pieters: 7
Glenn Whelan: 8
Charlie Adam: 6
Marko Arnautovic: 7
Bojan Krkic: 8
Xherdan Shaqiri: 8
Joselu: 6
Substitutes
Marco van Ginkel (on for Adam 70 mins): 6
Ibrahim Afellay (on for Arnautovic 75 mins): 6
Stephen Ireland (on for Bojan 79 mins): 6
STAR MAN
Xherdan Shaqiri: Brought a touch of class to a game where graft outweighed craft
Two lovely balls into the right-hand channel almost paid off and was a constant thorn to the Swansea defence, even if his shooting was slightly off
Troubled Neil Taylor throughout and the Wales defender will be glad to see the back of him.
MOMENT OF THE MATCH
Stoke capitalised on errors in the Swansea defence to strike in the third minute
Cork's mistake allowed Bojan to expose Swansea's centre-backs, easing past Federico Fernandez before tempting Ashley Williams into a rash challenge
The finish from the penalty spot was just as impressive - he never looked like wasting the opportunity.
VIEW FROM THE BENCH
Garry Monk opted to give the quicksilver but raw Modou Barrow only his second Premier League start to energise the Swansea frontline
Gylfi Sigurdsson paid the price for being out of sorts of late but Swansea rarely found any fluency
Mark Hughes has his Stoke side well drilled and he will be delighted that his attacking additions Bojan Krkic and Xherdan Shaqiri are now building on that solid base.
MOAN OF THE MATCH
Why do goalkeepers seems to get away with things that outfield players can not? Jack Butland's studs up challenge on Andre Ayew might have merited a red card had it come from any of the 20 outfield players on the pitch
Butland took the ball but it was reckless and could even have been a leg-breaker had Ayew not taken evasive action.
WHO'S UP NEXT?
Aston Villa v Swansea (Barclays Premier League, October 24)
Stoke v Watford (Barclays Premier League, October 24)
Source : PA
Source: PA