Marsh, playing his first match of the series, hit one six and 11 fours in his impressive 80-ball knock.
Sri Lanka were earlier 95-3 following a 71-run stand for the third wicket between Mahela Jayawardene (53) and Kumar Sangakkara (31), but lost their last seven wickets for 37 runs in a dramatic collapse.
Skipper Tillakaratne Dilshan (12) was the other batsman to reach double figures in Sri Lanka's dismal performance on a slow wicket.
"We bowled well but cannot ask bowlers to defend 130 against a strong batting line-up.
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I think Prasanna has a good future," said Dilshan.
Jayawardene, dropped on 34 by wicket-keeper Brad Haddin off paceman Mitchell Johnson, hit just four boundaries in his patient 102-ball knock before falling to Lee in the 39th over.
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Lee and Doug Bollinger did not allow Sri Lanka to make a solid start after the hosts elected to bat as they struck in their opening spells, removing Dilshan and Upul Tharanga (eight).
Sangakkara, hit on the helmet by a Bollin