The Swans suffered their first home defeat of the season after Bojan's early penalty earned Stoke a 1-0 victory at the Liberty Stadium.
The Spanish striker's third-minute effort was enough to separate the two sides on a frustrating night under the lights for Garry Monk's side.
Following the international break, the Swans struggled to find their usual fluency against a resolute Stoke defence.
Swansea's best effort came in the second half when Jonjo Shelvey saw a driven effort cannon back off the post, while substitute Gylfi Sigurdsson went close with a dipping long-range effort that fizzed just past the post.
The defeat sees the Swans drop to 14th in the Barclays Premier League with ten points from nine games.
The Swans made two changes to the starting XI.
Modou Barrow made his first start of the season with the Gambian handed an opportunity on the wing as Andre Ayew moved inside behind Bafe Gomis.
The other change saw Jack Cork return to central midfield as Ki Sung-Yueng - who travelled more than 13,000 miles while on international duty - moved to the bench along with Gylfi Sigurdsson.
Angel Rangel retained his place at right-back with Kyle Naughton among the substitutes after he missed the draw with Tottenham due to the birth of his daughter.
The Swans were without winger Wayne Routledge, who missed out with a minor calf injury.
Stoke were missing Ryan Shawcross, who was continuing his recovery from injury, while Mame Diouf was on compassionate leave.
Keeper Shay Given was sidelined with a knee injury though record signing Xherdan Shaqiri was back in the starting line-up after missing the 1-0 win over Aston Villa.
Lukasz Fabianski, Angel Rangel, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Jack Cork (Ki Sung-Yueng, 59), Jonjo Shelvey, Andre Ayew (Eder, 80), Modou Barrow (Gylfi Sigurdsson, 59), Jefferson Montero, Bafe Gomis.
Kristoffer Nordfeldt, Kyle Naughton, Kyle Bartley, Leon Britton.
Jack Butland, Erik Peters, Glenn Whelan (capt), Glen Johnson, Marko Arnautovic (Ibrahim Afellay, 75), Joselu, Charlie Adam (Marko Van Ginkel, 70), Geoff Cameron, Xherdan Shaqiri, Philipp Wollscheid, Bojan Krkic (Stephen Ireland, 79).
Jakob Haugaard, Marc Muniesa, Marc Wilson, Peter Crouch.
Under the floodlights of the Liberty Stadium, the Swans got off to a poor start as Bojan scored from the penalty spot to put the visitors in front inside three minutes.
The Spanish striker kept his cool from 12 yards to slot the ball into the top corner after he was fouled inside the box by Swans skipper Ashley Williams.
After regaining their composure following their early setback, the Swans posed a threat going forward as Bafe Gomis saw a looping header drop just wide, while Stoke goalkeeper Jack Butland was nearly left red-faced when Andre Ayew almost capitalised on the English stopper's badly mishit clearance.
Butland was then called into action to deny a long-range effort from compatriot Jonjo Shelvey, before Glen Johnson dragged wide of the target and Charlie Adam blazed over at the other end.
HALF-TIME: Swans 0 Stoke City 1
The Swans continued to probe early on in the second half but lacked the fluency and incisiveness that has been so key to their impressive home form so far this season.
Shortly before the hour-mark, Stoke's Marko Arnautovic thought he had doubled the visitors' advantage when he found the back of the net from close range, only to see his effort ruled out for offside, before Shelvey had Swansea's best chance of the game with a rifled effort that cannoned back off the post with Butland beaten.
In an effort to find a way back into the game, Swans boss Monk introduced Gylfi Sigurdsson and Ki Sung-Yueng into the fray, replacing Modou Barrow and Jack Cork.
And Sigurdsson went desperately close to making a stunning impact when he unleashed a fierce effort from 25 yards that flashed just past Butland's far post.
With the minutes dwindling away and Stoke sitting deeper and deeper, the Swans persisted to huff and puff to find a breakthrough, but despite their intent, the visitors were able to hold firm.