Australia were battling to increase their scoring rate when Marsh arrived at the crease, but the all rounder struck seven sixes in a 51-ball innings to help his side take 94 runs from the last eight overs.
Marsh's big hitting included three successive sixes off the bowling of Dale Steyn - the first time that the fast bowler had conceded that many sixes in a single ODI over.
Australia's innings had been pedestrian up until that point, with Phil Hughes rarely getting into his full stride in the course of his 85 from 92 balls.
Although Hughes put on 85 for the second wicket with Steve Smith, who returned to the Australian side and batted at No. 3 in the absence of the injured Michael Clarke, the spin duo of Imran Tahir and Aaron Phangiso picked up three cheap wickets.
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Phangiso recorded figures of two for 39 in his 10 overs, and his dismissal of skipper George Bailey left Australia 187 for five in the 42nd over.
However Marsh came to the rescue with his heavy hitting, which gave Australia something to bowl at.