The Irish reached 80 without loss chasing Australia's total of 231 for nine but James Hopes took five wickets to halt their momentum and the hosts subsided to 192 all out at the Clontarf Cricket Club.
Medium-pacer Hopes completed figures of five for 14 off nine overs after William Porterfield and Paul Stirling had given Ireland a fine start with bright knocks of 39 and 36.
Stirling eventually lost his leg stump to Ryan Harris and Porterfield was dismissed by Nathan Hauritz.
John Mooney struck a late 38 for Ireland but the damage had been done as they slumped from 80 without loss to 156 for nine.
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Opener Tim Paine was Australia's top run scorer with 81 from 122 balls and captain Ricky Ponting made 33. Australia never really dominated Ireland's attack, however, and needed a punchy 42 from Cameron White to post a testing target.
Kevin O'Brien was the pick of Ireland's bowlers, taking three wickets for 43 runs.
The world champion Australians face England in a five-match one-day series starting Tuesday.
