New Zealand scored 2-162 as Plimmer made a career high 85 off 68 balls and Green 56 from 37 balls, combining for 127 from 80 balls after the White Ferns had a difficult start on Sunday night.
They lost Flora Devonshire for just one and captain Melie Kerr for nine from 12 balls, to leave the White Ferns 2-35 from 6.4 overs.
Devonshire charged Kim Garth and was bowled by a fine inswinger, while Kerr was brilliantly caught scooping a full toss from Annabel Sutherland that was taken at ground level by Lucy Hamilton running in from fine leg and diving full length.
It was a breakout innings for the 22-year-old Plimmer, her fourth T20 half-century in 54 matches for New Zealand.
Going into the game she had an average of 16 and a strike rate of 104.
She was the beneficiary of two difficult chances, a stumping and catch from wicketkeeper Beth Mooney standing up to seamers Sutherland and Hamilton.
This is a new look White Ferns side following the retirements of key veterans Sophie Devine, Suzie Bates and Lea Tahuhu following a disappointing T20 World Cup campaign in the UK last June and July.
In contrast, Australia had won their last 10 Twenty20 Internationals, the most recent of which was an emphatic victory over England in the T20 World Cup final at Lord's in July.
No longer a T20 regular, Tahlia McGrath has regained her place after top order batter Phoebe Litchfield failed to recover from a hip strain suffered during the one-day series against Bangladesh last week in Brisbane.
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