Steve Smith and Joe Burns crafted centuries, broke records and made New Zealand's quicks "cook" as they dominated day two in Christchurch.
Australia were 4-363 at stumps on Sunday, trailing NZ by seven runs in the second trans-Tasman Test.
Smith and Burns reignited the tourists' hopes of regaining the No.1 Test ranking in a 289-run stand, Australia's highest ever in NZ.
Australia resumed on 1-57 then slipped to 2-67 after Usman Khawaja was out edging in the fourth over of the day.
What followed was leadership personified from Smith and desperate determination from Burns, who ended any lingering debate about his place in the XI.
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Burns' 170 represented the highest score by an Australian opener in NZ, while the 14th ton of Smith's 41-Test career was one of great courage given he was struck on the helmet.
Smith scored 138, having been crunched by a bouncer from Neil Wagner in the final over before tea.
The duo had a simple plan: expose the hosts' lack of a spinner by tiring out their four-pronged pace attack.
"We were aware that if we kept them out in the field, they'd just naturally get tired without a spinner to come on," Burns said.
"We kept talking about it all day, that we would just try to cook them for as long as possible.
"There's still so much time left in the game."
It wasn't exhilarating in the way Brendon McCullum was on day one, when NZ's retiring skipper smashed the fastest-ever Test century.
But it was effective; the sort of cricket lesson dished out so often during Steve Waugh's successful reign as skipper.
"It definitely slowed down quite a bit and the wicket flattened out," Wagner said.
"It was tough graft out there.
"We had to fight really hard."
Smith and Burns were incredibly watchful, shouldering arms and striking only the balls they wanted to.
The Black Caps' pace attack of Trent Boult, Tim Southee, Matt Henry and Wagner charged in throughout the day.
They tried plans A through to Z before Smith and Burns finally fell late in the final session.
Both batsmen will be unhappy with their method of dismissals: near-identical hook shots to near-identical deliveries from Wagner that resulted in near-identical Martin Guptill catches.
But they left Australia well placed to avoid defeat, an outcome that will take the team to top spot on the International Cricket Council's rankings.
Burns and Smith were unconvincing early but the runs came more freely after a testing opening hour.
Henry had Burns caught behind on 35 but the opener successfully used the Decision Review System to overturn his dismissal.
"I was confident I was not out," Burns said.
Part-time offspinner Kane Williamson delivered five overs as McCullum tried everything to conjure a wicket.
NZ pundits are already questioning the merits of dropping tweaker Mark Craig.
