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.
Voges reached his century from the penultimate over of the day.
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.
Voges wasn’t giving much away about the final day’s plan, noting the flat nature of the wicket.
“I don’t think we will do them any favours,” he said.
“Ultimately that will be Steve’s decision but the good thing is we have some options.”
Taylor said he expected Australians to set the Kiwis a target.
“The odd ball’s doing a little bit to put the batter a little bit on edge,” he said.
“But knowing Australia, I’m sure they’ll come out tomorrow and try to score some quick runs and put us under pressure.
“I’m sure whatever they give us, we’ll definitely have a go, and we’ll wait and see what happens. ”
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.
That made it a record combined first innings total for a Test at the WACA Ground.
Kiwi hopes were then raised when Australian openers Joe Burns (0) and David Warner (24) fell early, leaving the home side precariously placed at 46 for two, with the injured Usman Khawaja (hamstring) not taking his place at number three.
The Kiwis were still 19 runs ahead at that stage, but Smith and Voges then added 212 runs for the third wicket.
Taylor was the last man to fall in the New Zealand innings as he attempted to join captain Brendon McCullum (302 v India) as only the second Kiwi to reach a triple century in Test cricket.
However, on 290 the right-hander holed out to substitute fielder Jonathan Wells off spinner Nathan Lyon to end a 37-run 10th-wicket stand with Trent Boult (23 not out).
Former skipper Taylor passed several milestones in his innings, which was his first century since November last year, and ended a form slump that even he admitted was starting to worry him.
He broke through 5,000 Test runs and posted the highest-ever score by a visiting player in a Test in Australia, as well as becoming the first Kiwi to pass 200 against Australia.
His innings, beating the 287 of England’s Reg ‘Tip’ Foster at the Sydney Cricket Ground in 1903, was the third-highest ever for New Zealand at Test level.
Taylor, who put on 265 for the third wicket with Williamson, faced 374 balls and hit 43 boundaries in 567 minutes at the crease.
Number 10 Southee gave the Kiwis a lead which seemed impossible on the opening day when he turned Mitchell Starc off his pads for four as they became the first visiting side to reach 600 in Australia since 2011.
Starc was the best of the Australian bowlers and finished with four for 119.