The target in Sydney is 275 in 48 overs, the prize is a 4-1 series win and the ODI world No.1 ranking.
A win over South Africa in the fifth and final ODI will help Australia claim the No 1 ranking in Sydney on Sunday.
Australia recover from 5-98 to chase down 268 and win the Carlton Mid ODI series, now the host hold an unassailable 3-1 lead in the five-match series.
Trailing 2-1 in the five-ODI series, South Africa go into the fourth one-day international at the Melbourne Cricket Ground with an aim to level the series and give themselves a fair chance to win the trophy when they meet for the final ODI in Sydney.
Finch scored century, Mitchell Starc and Josh Hazlewood share seven wickets as Australia go 2-1 up.
Australia and South Africa head to the Manuka Oval with one all on the series and the other on the World Cup.
Australia squad named on Monday for the final three one-day internationals against South Africa, in Canberra, Melbourne and Sydney this month.
Morne Morkel rips through Australia's batsmen to level the ODI series at 1-1.
Australia look to continue their dominance against South Africa for the second time in Perth on Sunday.
Nathan Coulter-Nile and George Bailey hand Australia a 1-0 lead in the five match ODI series.