After winning the toss and choosing to bat, Australia quickly got into their work, with openers captain Alyssa Healy and Phoebe Litchfield - who made 50 from 59 balls - posting an 88-run opening partnership at more than six runs an over.
Despite the best efforts of Amelia Kerr and Rosemary Mair, who picked up two wickets each between the 15th and 22nd overs, Australia were able to regroup when Annabel Sutherland, who scored 42, and Ashleigh Gardner combined for a 73 run partnership for the fifth wicket.
Gardner in particular looked in classy form as she scored 74 from just 62 balls, before finally being bowled by Kerr.
The allrounder finished the best of the Kiwi bowlers, taking four for 54 from her 10 overs, while Mair took finished with three for 58 off her 10.
New Zealand claimed a moral victory by bowling out Australia with the last ball of the 49th over, but Australia had racked up 290 by then, which was to prove too challenging for the home team, despite all of the top five batters getting starts.
Opener Suzie Bates top-scored with 53 from 59 balls, the 49th time she has passed 50 in ODIs.
But once captain Sophie Devine was bowled by Darcie Brown for 25 - the fourth wicket to fall - the required run rate was already at a steep seven runs an over, and New Zealand were not able to offer a comeback.
Sutherland, who was player of the match and the series, and Alana King were the best of the Australian bowlers grabbing three wickets each, as New Zealand was dismissed for 215 in the 44th over.
The result has left Devine in a reflective mood.
"We were in the fight, and then unfortunately we fell away in the back 20 [overs] which you can't afford to do against a team like that, but we know there are some positive signs there," she told TVNZ.
The win means the Australians retained the Rose Bowl Trophy two games to nil, after also winning game two on Saturday by 65 runs.
The first of the three matches was abandoned without a ball bowled last Thursday.
Australia's skipper Healy was delighted with her team's form in the series.
"I thought it was an excellent performance, and I think our depth with both bat and ball has been on show," she told TVNZ.
New Zealand last held the trophy in 1999.
