After Ross Taylor hit a career-best 290, the highest score ever by a visiting batsman in Australia, to steer New Zealand to a first innings lead, Steve Smith and Adam Voges posted twin centuries to help the home side recover after a shaky start.
At the close, Australia were 258 for two in their second innings, with Smith on 131 and Voges on 101, for an overall lead of 193.
It was Smith's 12th century and fifth this year, but his first in a second innings, while for 36-year-old Voges it was just his second hundred and came in his first Test on his home ground.
Smith was dropped on 96 when wicketkeeper BJ Watling put down a tough chance down leg-side off paceman Matt Henry.
Although the match appeared set to be a draw on a lifeless wicket which has offered little assistance to the bowlers over the first four days, Australia will hope to declare on the final day and dismiss the Kiwis cheaply.
Australia already lead the three-Test series 1-0 after beating New Zealand by 208 runs at the Gabba.
In reply to Australia's imposing 559 for nine declared after winning the toss, the Kiwis were dismissed for 624 just before lunch, their highest total against their trans-Tasman rivals on the back of Taylor's mammoth knock and 166 from Kane Williamson.
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