After being outplayed in the first game in Melbourne, the White Ferns took control of the second and third games, rounded off by the second biggest-ever margin of defeat for the three-time World champions in the shortest format.
Chasing 114 to win the match and the series, Australia slumped to be all out for to 66, after at one stage being 9-5.
A pair of run-outs topped and tailed a disastrous innings, as Lea Tahuhu, Holly Huddleston, and Amelia Kerr shared six wickets between them.
Huddleston picked up the critical wicket of captain Meg Lanning in the fourth over of the Australian pursuit.
New Zealand's innings had been underpinned by firm starts from Priest, Amy Satterthwaite and captain Suzie Bates.
Bates' was named Player-of-the-Match and the Player-of-the-Series honours.
Australia and New Zealand now move into 50-over mode for the Trans-Tasman Rose Bowl series, the first of which is in Auckland on Sunday.