The left-handed opener smashed an unbeaten 75 as Australia made it to the target of 138 with a whopping 39 balls to spare.
Mooney and fellow opener Georgia Voll (50) blasted Australia to 0-77 from just six overs to stun the reigning T20 world champions at Eden Park on Friday.
New Zealand were rattled by the ferocity of the batting, making a series of uncharacteristic mistakes in the field that made the result a formality.
It was Australia's highest opening partnership in a T20 against New Zealand.
Voll fell just 15 runs away from the target and Phoebe Litchfield also was dismissed, before Ellyse Perry helped Mooney steer Australia home.
The Aussies finished the job without star allrounder Ashleigh Gardner, who was sent for scans on an injured finger.
Mooney's performance in her milestone match was fitting because she has been a constant, but often underrated, member of the all-conquering Australian side for almost a decade.
"Eden Park's a pretty iconic venue in New Zealand, so first and foremost to do it here was pretty special, and I had a few close family and friends in the crowd, so that was nice as well," Mooney told reporters in Auckland.
"To play the way we did was probably the icing on the cake, for sure.
"We've just got this production line of young players ready to step up and perform in this team and they look like they've been here for years."
After electing to bat first, the White Ferns posted 2-137 on the back of an unbeaten 90-run partnership between Amelia Kerr (51no) and Sophie Devine (39no).
In her first international back after taking a mental break in December, star veteran Devine impressed at the crease with Kerr.
Stand-in captain Tahlia McGrath and quick Darcie Brown took Australia's only wickets.
In a blow for Australia, Gardner was sent for scans on her right index finger after leaving the field, replaced by Alana King.
Given it was a T20, Gardner was never going to be able to complete her scans, get the all-clear, then return in time to bat, if required.
Apart from being without injured captain Alyssa Healy, Australia picked a full-strength XI for the first of three games.
The White Ferns are the reigning T20 world champions after pulling off a surprise win at last October's tournament.
Australia, who had won the previous three T20 World Cups, were eliminated in the semi-finals and were desperate to reassert their dominance.
Star bowler King, player of the series in the recent Ashes thumping of England, was left out in preference of fellow legspinner Georgia Wareham.
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