However, there was again no answer to the final quarter points starvation diet they have endured throughout the Lipovitan D Rugby Championship. They were again guilty of losing discipline under pressure at vital stages.
Up 28-14 at halftime, the All Blacks demonstrated their latent attacking potential again, but their failure to seize chances again hit them hard. Australia's defence in the first half was poor, missing 23 tackles to seven.
However, the loss of replacement five-eighths Anton Lienert-Brown after the All Blacks were hit for too many penalties in their 22m area and wing Caleb Clarke for a deliberate knockdown allowed Australia back into the game.
While the All Blacks failed to eliminate their fourth-quarter scoring vacuum, the Australians emerged with credit. They turned around their heaviest defeat in Argentina in their last outing to get within three points of the All Blacks.
It was a nervous, if exciting finish, only achieved when they denied the Australians the chance to run out the final restart of the game.
No8 Ardie Savea and replacement halfback TJ Perenara won a turnover by holding up the Australian maul. Savea kicked the ball out from the resulting scrum to end the game.
It was frustrating for the All Blacks. TMO judgments ruled out three tries, and Australia missed out on one, similarly.
The All Blacks' ability to pick up crucial turnovers was a significant factor in their holding on to win. Savea was always prominent, but his blindside counterpart, Wallace Sititi, was outstanding throughout. Halfback Cortez Ratima also made an impact as the All Blacks threatened to run rampant.
They lost Jordie Barrett at halftime, when he suffered a knee injury in the act of scoring a try that was one of the trio of tries ruled out, and that upset the backline rhythm where he and centre Rieko Ioane gelled better than at any time in the season.
A 65th-minute try, scored by second five-eighths Hunter Paisami, narrowed the All Blacks lead to 10 points, with Lienert-Brown suffering his sin-binning.
No sooner had they scored than Australia stormed back from the restart, and it was a desperate cover tackle by replacement halfback TJ Perenara, moments after he earlier slammed a 60m kick from the All Blacks' goalline after a lineout steal.
The All Blacks started as if on a mission, quickly dismissing concerns about Beauden Barrett's enforced absence from fullback due to illness. It took only 1min 31sec to be allayed by his replacement, Will Jordan. He fielded the missed Australian kick to touch set the move in train, powering into a gap 35m out and racing away to score under the posts.
Even after an eighth-minute thumping in a tackle after taking the ball in the air, Jordan was able to pass the ball back. When Ratima ran from a ruck in midfield, he found space and passed on to Ioane unmarked out wide to score.
Intercepting an Australian pass, Clarke set in train a movement that unleashed more running play and punished poor Australian defence. When the ball returned to the left flank, Clarke burst through two tacklers to score in the 14th minute.
Finally, Australia got a break off a long lineout throw. Flanker Rob Valetini linked with halfback Nic White, who passed on to flanker Fraser McReight who scored.
Australian turnovers, especially at lineout time, and in the 24th minute, Paisami's pass went to grass; wing Sevu Reece claimed the ball, regathered his feet and passed to Savea, who scored with ease.
Five minutes from halftime, a scrum penalty allowed an Australian kick to the corner, and from the maul, hooker Matt Faessler came around to score.
Australia got a massive confidence boost from their effort, but next week's second Test at SKY Stadium for the All Blacks will be crucial in resolving their execution and final quarter issues before heading offshore for their northern hemisphere programme.
Scorers: Australia 28 (Fraser McReight, Matt Faessler, Hunter Paisami, Tom Wright tries; Noah Lolesio 4 con) New Zealand 31 (Will Jordan, Rieko Ioane, Caleb Clarke, Ardie Savea, Jordie Barrett tries; Damian McKenzie 4 con, pen). HT: 14-28