Leg-spinner Adam Zampa knocked over the middle order to finish with 4-34 as the home side were skittled for 102 in 17 overs at Eden Park.
New Zealand lost early wickets and always looked unlikely to match the visitors, who were dismissed for 174 in the final over.
Only Glenn Phillips provided resistance with 42 but New Zealand’s hopes were buried when he was caught at long-on off Zampa in the 14th over.
Australia captain Mitchell Marsh said he was worried his team hadn’t scored enough but was delighted with their bowling, with the T20 World Cup coming up in June.
“A great win for Australia. Our backs were against the wall, I thought we were probably 50 short but the way our bowlers performed was outstanding,” said Marsh, who praised the match-winning prowess of Zampa.
“I’ve said it so many times before — he’s probably the most important player in this team. He was brilliant again.”
The Black Caps’ cause wasn’t helped by a thumb injury suffered in the field by Devon Conway, which prevented the opener from batting.
The injury, sustained while he was wicket-keeping, may place Conway in doubt for Sunday’s third match in Auckland.
Captain Mitchell Santner said X-rays showed Conway hadn’t suffered a fracture and he hoped the experienced batsman would be available for the two-Test series starting next week in Wellington.
Santner praised his bowlers but said the batting effort lacked discipline.
He promoted himself up the order but that experiment failed and he was one of eight New Zealand batsmen who didn’t go past 10 as they fell to a succession of loose shots.
“We were pretty happy at halfway but they bowled extremely well,” he said. Earlier, opener Travis Head blazed 45 runs off 22 balls after Australia were sent in but they stumbled through the middle stages in the face of brilliant bowling from paceman Lockie Ferguson.
Ferguson claimed 4-12 from 3.5 overs as Head’s dismissal sparked the loss of five quick wickets after Australia had been 84-1 in the seventh over. Other notable scores were 26 from Marsh and a late 28 from player of the match Pat Cummins.
Santner, Adam Milne and Ben Sears all took two wickets each for the hosts.