Former Barcelona forward Bojan earned and converted a fourth-minute penalty which sealed a scrappy encounter and left Swansea without a league win since August.
Bojan was bundled over by Swans skipper Ashley Williams and he got up to send Lukasz Fabianski the wrong way.
Swansea hit the post through Jonjo Shelvey early in the second half but struggled to open up a resolute Stoke side who claimed their third successive league win to climb to 11th.
Swansea drop to 14th.
"Very disappointed with the result," Swansea boss Garry Monk said. "Once they got the goal it was clear they would defend very deep and that made it very difficult to break them down.
"We are in a period where we are not performing to those levels we had at the start of the season."
(Reporting by Martyn Herman; Editing by Rex Gowar)
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