Marnus Labuschagne scored a maiden double century to drive Australia to 454 all out before New Zealand's openers resisted the home attack to post 63 without loss on the second day of the third test on Saturday.
Tom Latham, standing in as captain for the sick Kane Williamson, had made 26 not out at the close of play with Tom Blundell unbeaten on 34 but the tourists know they still have a mountain to climb if they are to avoid a 3-0 series sweep.
Labuschagne is a large part of the reason for that and a hot, sunny day at the Sydney Cricket Ground belonged to the irrepressible 25-year-old, who has enjoyed a golden summer in Australia's home season.
He had a nervous 20 minutes one run short of the double century mark but his 19th four got him over the line and earned him a standing ovation from the crowd.
He finally departed for 215, caught and bowled by spinner Todd Astle, and left the field to another huge ovation having scored 837 runs at an average of 119.57 in five home tests this season.
Labuschagne faced 363 deliveries in a magnificent innings that looked to have set Australia well on their way to another victory to add to the thumping wins they enjoyed in Perth and Melbourne.
"It was a good day personally but more importantly a good day for Australia," Labuschagne said.
"They fought back, as you would expect, but we'll do the toil and hopefully get the win."
New Zealand made short work of the tail after Labuschagne's exit to dismiss the hosts and bring up tea before their openers headed back out to face Australia's in-form pacemen.
The Black Caps have accumulated only one score in excess of 200 runs in their previous four innings in the series but Latham and Blundell saw off the attack and scrapped their way to stumps.
"It was nice to turn up and show that fight today," said Astle. "It's gonna be a tough ask but that's what this group's about. We'll keep grinding away."
There had been concerns that soaring temperatures forecast for Saturday might worsen the bushfire emergency around Australia and the blanket of acrid smoke that has covered Sydney on several occasions in recent weeks might return.
Labuschagne, however, resumed his innings on 130 under blue skies and was soon passing 150 for the third time in his last seven innings.
With Australia utterly dominating all five home matches this year, their fans have had precious little drama to enjoy so it was perhaps understandable that they made the most of Labuschagne's progress through the 190s.
"Being in the 190s is a bit different to being in the 90s, you're just trying to avoid doing something stupid," Labuschagne added.
The crowd were kept waiting for four overs with Labuschagne stuck on 199 and there were good-hearted boos for captain Tim Paine when he scored a single off the final ball of one to keep the strike for the next.
New Zealand pulled in the field to deny him the single and it worked for seven deliveries until he swiped at a Colin de Grandhomme delivery and got a thick edge that sent the ball racing to the boundary.