Speed and accuracy through midcourt allowed the Ferns to set the pace, as Claire Kersten led from the circle edge, finding the hands of her shooters with ease.
Improved ball retention was pivotal, as New Zealand capitalised on Australia's errors.
The Diamonds were hammered in the penalty count and gave up 27 turnovers to New Zealand's 18. The Ferns used that possession more effectively, scoring off half their turnovers gained, compared with only 21 per cent from the Diamonds.
Ferns defender Jane Watson put her aerial game on display against the towering Caitlin Bassett — and although the Australian shooter was accurate under the post, scoring off 19 of her 21 attempts, her opportunities were limited.
Watson was supported superbly by Sulu Fitzpatrick, as the defensive pair set up tricky zone defence to help the hosts to a seven-goal advantage at halftime.
Gina Crampton had a strong night, leading her side in feeds and goal assists, and was second to only Ameliaranne Ekenasio on centre pass receives.
The third quarter started much the same before a brief swing in momentum saw coach Dame Noeline Taurua look to her bench, with Karin Burger added to the defensive mix — it worked, and the Ferns regained control to sit comfortably for the final 15.
Sam Winders was energetic throughout the midcourt as Taurua's fit Ferns stormed on, although the Diamonds finished strongly to cut the gap to five at fulltime.
Australia boasted better shooting accuracy, but New Zealand's weight of shots was telling, with Maia Wilson converting 31 of 40, and Ekenasio 18 of 23.
Ferns captain Ekenasio was pleased with her side's first hit-out of the year.
"It feels really good. We really wanted the first game, it was tough at times but that's what we expected," Ekenasio said.
"We have a ton of stuff to work on, we did let them back in at times, but there's also lots to celebrate.
"We're confident in our game plan and I'm happy with how we got stuck in and retained the ball when it mattered."
The second of their four-match series, put on hold last year due to Covid-19, will be played on Wednesday night.