The 58-50 victory gives the Diamonds a 2-1 lead in the series with two tests to play.
Kim Green was brilliant for the Aussies at wing attack and then centre, while Cailtin Bassett and Natalie Medhurst shot well all night, Medhurst in her 50th appearance for the national team.
For the Kiwis, legend Irene van Dyk was on fire early, hitting with 18 from 19 attempts before being subbed out at three-quarter time, the Silver Ferns trailing by 13 and appearing to concede the game.
Goal attack Maria Tutaia toiled hard but went missing at key moments in the third quarter, largely thanks to the close attention from Aussie goal defence Bianca Chatfield.
Centre Laura Langman was probably New Zealand's best on the night, while Shannon Francois was also good when subbed in for the second half.
Captaining the team for the first time on home soil, Laura Geitz seemed nervous early, giving up a string of penalties but had the better of the Kiwi attack in the second half.
As well as a key game in the series, the win takes the Diamonds' head-to-head record against the Silver Ferns to 67-45 and continues the national team's winning streak in Adelaide where they have been not been beaten for more than 20 years.
Geitz said the team stuck to its game plan but still believed they could improve in the next test in Melbourne on Monday.
"There's obviously a few things we can work on," she said.
Star Silver Ferns defender Leana de Bruin was a late withdrawal from the game after injuring a calf in training on Wednesday.
She was initially named on the bench but coach Waimarama Taumaunu elected not to risk her with two tests still to play.
Taumaunu said she was pleased with the effort but said the Kiwis still needed to cut down on errors and improve the shooting percentage.
The Silver Ferns made 50 from 59 at 85 per cent, to the Aussies 58 from 62 at 94 per cent.
"We struggled to get the ball through to the attack line and we struggled with the physical pressure that Australia put on us," she said.
"But the Australian shooting circle was outstanding tonight.
"We just need to keep working away at that. Our target used to be 85 (per cent) but when you've got a team shooting at 94 per cent, it has to lift."
New Zealand captain Casey Kopua said the Kiwis still believed they could win the series.
"We've got nothing to lose and pretty much the next game is do or die," she said.
"We have to leave everything out there and do everything possible when we get to Melbourne to make it happen."
Australian coach Lisa Alexander said the improvement after the narrow win in Auckland last month came down to reducing turnovers and working hard on defence.
"We just took our opportunities tonight," she said.
"We really seemed to understand that we wanted to keep the momentum after we got the turnovers."
Geitz said the win gave the Diamonds plenty of confidence heading to Melbourne, both because of the defensive strength and the shooting of Bassett and Medhurst.
Bassett scored 40 from 43 attempts and Medhurst 18 from 19 in a performance which belied the little time they've played together.
"We're winning the ball but we know they they're converting it," Geitz said.
"It's just pretty to watch."
