After New Zealand A were bowled out for 147, Australia A went to stumps on day one of the four-day match at 3-141 with the game firmly in their control.
Swepson (3-19) and South Australian Jordan Buckingham (3-29) each took three wickets in the rout, while Queenslander Mark Steketee picked up 2-29.
Australia's second spinner alongside Nathan Lyon in Pakistan and Sri Lanka last year, Swepson has fallen down the pecking order over the past 12 months.
The Queenslander was not picked for the first two Tests in India, before flying home for the birth of his child.
His replacement Matthew Kuhnemann immediately earned a Test debut, while Todd Murphy claimed 14 wickets on the tour as second spinner to Lyon.
Swepson was overlooked for Australia's Ashes tour squad, where Murphy took the mantle of chief spinner after Lyon's calf injury.
But playing in his first red-ball match in Australia since then, Swepson cleaned up the New Zealanders' tail with three wickets in his 4.5 overs.
With the bat, Cameron Bancroft missed an early chance to make a statement in the race to replace David Warner as Australia's next Test opener when he was caught behind on 14.
Tim Ward and Nathan McSweeney also fell for 16 and 22 respectively, before Caleb Jewel took charge for Australia A to go to stumps unbeaten on 69.
The unofficial Test is one of two between the two teams in Queensland, before three 50-over games.
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