Opener Finch ran out of partners and he was the last man out in Australia A's run chase of 253 for a win. His 129-ball innings was studded with 10 fours and four sixes.
Nic Maddinson was the other notable contributor as Australia 'A' were shot out for 233 in 42.2 overs.
For South Africa 'A', Rusty Theron took four wickets for 51 runs while Hardus Viljoen chipped in with three scalps.
Earlier, opting to bat, South Africa 'A' were 252 all out in 47.4 overs. Dean Elgar (52), Dane Vilas (55) and Theron (53) struck a half century each.
This is the first win for South Africa 'A' in three matches. They had lost a game each against Australia 'A' and India 'A' before today's match.
For Australia 'A', today's was their first loss in three matches having won against South Africa 'A' and India 'A' earlier. India 'A' have won one -- against South Africa 'A' --and lost one -- against Australia 'A'.
Brief Scores:
South Africa 'A': 252 all out in 47.4 overs (Dean Elgar 52, Dane Vilas 55, Rusty Theron 53; Gurinder Sandhu 4/51)
Australia 'A': 233 all out in 42.2 overs (Aaron Finch 119; Rusty Theron 4/51, Hardus Viljoen 3/63).
South Africa A beat Australia in tri-series despite Aaron Finch's century
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