The hosts resumed on 416-2 and despite losing seven wickets while adding 143, they still declared on a massive 559-9.
David Warner edged to second slip after adding only nine to his overnight 244.
New Zealand soon lost openers Martin Guptill and Tom Latham but Kane Williamson (70 not out) and Ross Taylor helped them to 140-2 at the close.
Taylor made an unbeaten 26 as the third-wicket pair shared an unbroken stand of 53, fending off the Australian attack with a stubborn rearguard action.
That partnership is expected to be key if their side are to make significant inroads into a deficit which still stands at 419.
New Zealand are already 1-0 down in the series, having lost the opening Test in Brisbane.
The declaration came not long after off-spinner Mark Craig (3-123) picked up the wickets of Peter Nevill, Mitchell Starc and Mitchell Johnson in the same over, all three falling with the score on 547.
However, Starc then struck in the third over when he trapped Guptill lbw for one, while Latham (36) added 81 with Williamson before he was caught at slip.
However, there was some concern for Australia with batsman Usman Khawaja now a doubt for the day-night Test in Adelaide later this month
Khawaja, 28, scored 121 in Australia's first innings but re-injured his left hamstring while fielding on Saturday and will undergo a scan on Sunday.
"My fingers are crossed that he can try and recover in the next 10 to 15 days," said Warner.
"[Having scored] back-to-back hundreds, and running a lot out in the middle, and fielding at mid-off as well - having to chase a hell of a lot of balls to the boundary - is not ideal.
"But that's part and parcel of this game. It can be quite challenging."
Listen to ball-by-ball commentary of every day of the Test series on BBC Radio 5 live sports extra from 02:05 GMT.

The company's roots date back to the 1930s, when Greece's National Radio Foundation was set up.
The many decades of history behind ERT have made it a well-established national institution respected by many.
It began airing television programmes in the 1960s, remaining the country's only TV broadcaster until the advent of private TV channels in 1989. Since then, ERT has undergone several major overhauls to keep up with fierce private competition.
These efforts were not entirely successful, and a fall in the company's ratings in the mid-1990s triggered a long-running debate about its cost and efficiency.
Eighty per cent of the company's funding came from a licence fee included in electricity bills, and some of it was sourced from advertising revenue.
Many Greeks objected to funding ERT through the licence fee, claiming that the company was too unpopular and too expensive. The broadcaster was also criticised for its openly pro-government reporting, especially since the start of the financial crisis in 2009.
At the time of closing, ERT operated three main TV channels and more than a dozen national and local radio stations. ERT World TV catered for the Greek diaspora across the globe.
The company's programming included news as well as factual and entertainment programmes. It claimed to broadcast more highbrow programmes - such as world cinema and documentaries - compared to the generally more light-hearted entertainment offered by its privately-owned rivals.
The company's audience share in 2013 was relatively low at below 20%, with most Greeks preferring commercial broadcasters.
The government's surprise decision to shut down ERT was, however, met with fierce criticism from the public. Even though most agreed that a restructuring and cost-savings were required at the company, its immediate closure was branded "dictatorial" by some.
While most Greeks will continue getting their news and entertainment from private TV and radio stations, those in the east and some islands - where signal coverage is poor - may have to rely on Turkish broadcasters across the border.
BBC Monitoring reports and analyses news from TV, radio, web and print media around the world. For more reports from BBC Monitoring, click here. You can follow BBC Monitoring on Twitter and Facebook.
Australia maintained their commanding position on day two of the second Test of their three-match series against New Zealand in Perth.
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On 11 June, the government in Athens unexpectedly announced it was suspending the country's Radio and Television Company, abbreviated to ERT in Greek, as part of drastic budget cuts.