Bulls left-arm paceman Liam Guthrie (4-15 off eight overs) set up the victory at Allan Border Field as the visitors were bowled out for 218 with McSweeney (137 off 131 balls) playing a lone hand.
The Bulls chased down the total with ease in the 33rd over to secure a bonus point with wicketkeeper Jimmy Peirson middling an array of pulls, cuts and drives in a blistering unbeaten 100 off 98 balls.
"Personally I am in a great spot with my technique and how I am going about my business and it was so nice to get a win," Peirson told AAP.
"I missed out on selection for the first couple of one-dayers and had real grit between my teeth to do the job today. It was so great to get it done."
Usman Khawaja (42) played a key role early before Test hopeful Matthew Renshaw found confidence and form with a whirlwind unbeaten 72 off 52 balls,.
Earlier Guthrie (4-15 off eight) bowled the dangerous Jake Fraser-McGurk (2) with an inswinger and his three quick wickets in six pinpoint overs put the hosts on top.
At the other end, Tom Straker (3-54) got rid of the dangerous Alex Carey (6) and brought McSweeney to the crease at 2-9.
South Australia were 4-29 in the 12th over and on the rack. McSweeney had initial support from Thomas Kelly (29) in the middle order in a 90-run stand for the fifth wicket.
After that, wickets tumbled as McSweeney unfurled an assortment of sweetly timed cover drives both over and through the infield as the skipper made it appear as though he was batting on a different pitch to his teammates.
"One of the finest knocks we have seen in one-day cricket," former Australia coach and batter Darren Lehmann said in commentary.
Lehmann is pushing for either McSweeney or NSW opener Sam Konstas to partner Khawaja at the top of the order in the Test series against India.
McSweeney will captain the Australia A side against India next week in Mackay. Peirson will join the side for the second game in Melbourne.
He is behind Alex Carey and Josh Inglis in the Australian pecking order and is close to national honours.
"George (Bailey) has been very clear that is how they see things at the moment," Peirson said.
"Alex has been doing the Test job, Ingo is behind him nipping at his heels and I am behind Ingo. It is a healthy place to be. I am very clear about where I stand. You are always pushing to get yourself closer to play Test cricket.
"Any game for Australia A is a massive honour and there is no doubt runs on the board get you talked about. I am glad to link up with Buddha (McSweeney) again, a good Queensland boy."
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