Match ends, Swansea City 0, Stoke City 1.
Stoke City secured a third straight Premier League win to add to Swansea City's problems as Bojan's early penalty settled a scrappy encounter.
The former Barcelona forward sent Lukasz Fabianski the wrong way after he was bundled over by Ashley Williams.
Stoke, now 11th in the table, had chances to extend their lead through Glen Johnson, Charlie Adam and Joselu.
Jonjo Shelvey went close to equalising when his low, angled shot hit the inside of a post and bounced out.
Yet this was a distinctly under-par performance by Garry Monk's side, who drop to 14th in the table and are without a win in five league games.
Stoke were creative, industrious, dogged and determined as they dominated the opening 45 minutes.
The hosts rallied after the break, substitute Gylfi Sigurdsson going close with a dipping shot soon after Shelvey had been denied by the woodwork.
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Worrying times for Monk
Monk deservedly won plenty of plaudits for leading Swansea to an impressive eighth-placed finish last season.
That was partly down to ruthless home form, with Arsenal and Manchester United among nine teams who left the Liberty Stadium without any points.
But these are worrying times for Monk and his players. The Swans look desperately short of confidence after a return of just two points from a possible 15.
Jefferson Montero, Bafetimbi Gomis and Andre Ayew were unrecognisable from their impressive early season form in a lacklustre team performance, a throwback to the latter days of Michael Laudrup's time in charge before the Dane was dismissed in February 2014.
Monk needs to get the Swans, who have an awkward trip to fellow strugglers Aston Villa on Saturday, firing quickly again.
"We went five games without a win last season. I'm not worried. We'll come through it no problem," said the Swansea boss afterwards.
Stoke's rapid rise
Stoke were left propping up the Premier League table with two points from five games after a 2-0 defeat at Arsenal on 12 September.
Yet Mark Hughes' side have moved above champions Chelsea and are only two points behind seventh-placed Tottenham after an impressive change in form.
They bossed Swansea from the start, with Williams' foul on Bojan a gift which cost their Welsh opponents dear.
Adam and Glenn Whelan were particularly impressive in midfield, with forwards Joselu, Bojan and Marko Arnautovic ensuring the home defence was overworked.
Against Swansea, there was little doubt of the outcome once Bojan scored.
However, there was a moment of concern when keeper Jack Butland came charging out and committed a studs-up challenge on Ayew which went unpunished.
The incident was replayed on the big screen inside the ground provoking a chorus of jeers from Swans fans.
"I was a little bit upset that the replay was shown in the stadium," said Hughes. "That shouldn't be allowed. It isn't allowed."
Man of the Match - Joselu
What they said
Swansea City manager Garry Monk: "We found it difficult to break them down. I think we deserved a point but I can't grumble with a defeat.
"We've had a month of not hitting those levels.
"They're very good players. I need to get them back to that level. I have big confidence in this group."
Stoke City manager Mark Hughes: "Sometimes you think you've scored too early. But we had control of the game.
"Maybe if we'd taken more care with the final pass we might have capitalised on more opportunities.
"They never really created anything of note. We've restricted them and created opportunities.
"Swansea never got any momentum in the game which was important. We're on a decent run of form."
The stats you need to know
- Stoke have won consecutive Premier League away games for the first time since December 2011.
- Swansea have failed to keep a clean sheet in six of their last seven Premier League fixtures.
- Stoke forward Bojan has found the back of the net in three of his last five Premier League starts on the road.
- The Swans have only won two of their last 11 league fixtures
- 6WilliamsBooked at 41mins
- 24CorkSubstituted forKi Sung-yuengat 59'minutes
- 8ShelveyBooked at 57mins
- 58BarrowSubstituted forG Sigurdssonat 59'minutes
- 10A AyewSubstituted forMacedo Lopesat 80'minutes
- 4Ki Sung-yueng
- 17Macedo Lopes
- 23G Sigurdsson
- 3PietersBooked at 45mins
- 16AdamSubstituted forVan Ginkelat 70'minutes
- 22ShaqiriBooked at 66mins
- 27BojanSubstituted forIrelandat 79'minutes
- 10ArnautovicSubstituted forAfellayat 75'minutes
- 15Van Ginkel
- Robert Madley
- Shots on Target
Second Half ends, Swansea City 0, Stoke City 1.
Offside, Swansea City. Jonjo Shelvey tries a through ball, but Bafétimbi Gomis is caught offside.
Attempt missed. Ki Sung-yueng (Swansea City) header from the centre of the box misses to the left. Assisted by Jefferson Montero with a cross.
Offside, Stoke City. Xherdan Shaqiri tries a through ball, but Joselu is caught offside.
Attempt missed. Eder (Swansea City) right footed shot from outside the box misses to the left. Assisted by Bafétimbi Gomis.
Eder (Swansea City) wins a free kick on the right wing.
Foul by Marco Van Ginkel (Stoke City).
Foul by Eder (Swansea City).
Joselu (Stoke City) wins a free kick in the attacking half.
Attempt saved. Ibrahim Afellay (Stoke City) left footed shot from outside the box is saved in the bottom right corner. Assisted by Erik Pieters.
Substitution, Swansea City. Eder replaces André Ayew.
Substitution, Stoke City. Stephen Ireland replaces Bojan.
Substitution, Stoke City. Ibrahim Afellay replaces Marko Arnautovic.
Foul by Jefferson Montero (Swansea City).
Xherdan Shaqiri (Stoke City) wins a free kick in the defensive half.
Substitution, Stoke City. Marco Van Ginkel replaces Charlie Adam.
Attempt missed. Gylfi Sigurdsson (Swansea City) right footed shot from outside the box is close, but misses the top right corner. Assisted by Jefferson Montero.
Attempt missed. Marko Arnautovic (Stoke City) right footed shot from the centre of the box is close, but misses to the right. Assisted by Xherdan Shaqiri with a through ball.
Attempt blocked. Bafétimbi Gomis (Swansea City) right footed shot from the centre of the box is blocked. Assisted by Ki Sung-yueng.