Finch was in blistering form as the Australians made full use of Canberra's slow Manuka Oval pitch after winning the toss.
Finch hit nine fours and three sixes to spearhead the Australian run plunder before he was dismissed by part-time bowler AB de Villiers in the 41st over.
Fellow opener David Warner pounded 53 off 50 balls with six fours and two sixes in a first-wicket stand of 118 in 20 overs.
Steve Smith hammered an unbeaten 73 from 55 balls in an innings full of shot improvisation, including one boundary hit through his legs.
Smith crashed eight fours in a majestic knock, while Shane Watson took a more controlled 40 off 38 balls before he miscued and was caught in the deep by David Miller off the medium pacers of Farhaan Behardien.
Skipper George Bailey came and went for 12 and Mitchell Marsh smacked 22 off 13 balls.
Morne Morkel was the best of the Proteas bowlers with two for 84, while Vernon Philander, de Villiers and Behardien all took a wicket each.
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