The Australians had already clinched the series after winning the first two meetings in Wellington and Auckland, and racked up 118 runs for four wickets in 10.4 overs that were repeatedly interrupted by rain.
Travis Head top scored for Australia with 33 runs from 30 balls before he was caught by Ish Sodhi off Mitchell Santner's bowling and New Zealand were set a target of 126 runs in 10 overs.
Opener Will Young fell in the second over, and with Tim Seifert and Finn Allen joining him in the pavilion soon, New Zealand's cause was all but lost.
Glenn Phillips smashed 40 not out off 24 balls but it was not enough in the end.
The bilateral series was the last international outing for both teams prior to the start of the Indian Premier League next month and June's T20 World Cup in the West Indies and the United States.
