Swepson ran through the hosts' tail on Saturday to have them all out for 308 in their second innings, leaving Queensland a fourth-innings chase of 139.
Usman Khawaja fell for a duck and Marnus Labuschagne was lbw for 18 following his first-innings century, but Angus Lovell (72no off 115 deliveries) ensured the Bulls won easily.
From day one at Adelaide Oval, Swepson was at the centre of Queensland's success, with 10 wickets for the match and second-innings figures of 6-109.
The former Test spinner did the bulk of the damage on the opening day for the Bulls, taking four wickets in a collapse that left South Australia falling from 2-11 to 7-188.
And after Labuschagne's 159 gave Queensland a 170-run first-innings advantage, it was Swepson who again did the damage on days three and four.
The legspinner took apart South Australia's top three, trapping both Conor McInerney (46) and Henry Hunt (36) lbw, before Nathan McSweeney (26) edged him to slip.
Then on Saturday Swepson beat Nathan McAndrew in flight to have him well caught by Hugh Weibgen running back at mid-off.
He also removed a sweeping Wes Agar caught behind on 19, before Lloyd Pope hit him straight to Weibgen at cover to end South Australia's second innings.
Swepson's haul was his second 10-wicket haul, after doing likewise against NSW in 2020.
At that point Swepson was considered the country's second-choice spinner, before falling back down the pecking order in recent years.
The 32-year-old's 6-109 in the second innings also marked his career-best figures, as Queensland made it one win and one draw to start the season.
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