At the close on day three, the home team were 137 for four
New Zealand were facing a massive run chase to save the second Test and the series after they were dismissed for 148 in Melbourne on Saturday, with Australia batting again to rub salt in the wounds and extend their lead.
At the close on day three, the home team were 137 for four, building on their first innings 467 to be 456 runs in front.
First innings century-maker Travis Head was not out 12 and Matthew Wade was on 15, with skipper Tim Paine so far resisting the temptation to declare.
New Zealand began the day already in trouble on 44 for two, having lost batting kingpin Kane Williamson and makeshift opener Tom Blundell in a fiery bowling spell late Friday.
They didn't survive long with a world-class pace barrage from Pat Cummins, James Pattinson and Mitchell Starc destroying their middle order.
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Their day was made worse by veteran quick Trent Boult's hand being fractured by a Starc bouncer, which will see him miss the third Test in Sydney.
"I was happy with how it all came out today. I feel like I have been bowling well, especially the last couple of games," said Cummins after his 5-28 haul. "Today it felt like it all came together."
Paine could have enforced the follow-on, but opted to bat again and Australia raced to 62 without loss before Neil Wagner tempted David Warner into a drive on 38 and he was caught by Blundell.
Marnus Labuschagne was run out for 19 and spinner Mitchell Santner snared opener Joe Burns for 35.
When Steve Smith departed for seven, Wagner's 200th Test wicket, the Black Caps were on a roll, but Head and Wade steered them to the close, leaving New Zealand with a monumental task.
They need a result to keep the three-Test series alive after being crushed by 296 runs in the opening day-night clash in Perth.
Opener Tom Latham was the only one to offer resistance in their first innings demolition, surviving 144 balls in a dogged 50 before he too succumbed to the Australian fast-bowling machine.
"It was pretty relentless. They didn't really let us have anything but that's Test cricket," said Latham. "The way they executed from a bowling point of view was spot on and we unfortunately didn't quite handle it the way we would have wanted to today."
They resumed with Latham on nine with Ross Taylor on two, but had a disastrous morning and went to lunch at 102 for six.
Taylor was removed in just the third over and Henry Nicholls followed for a golden duck as they crumbled under consistent pace and accuracy.
Cummins was virtually unplayable, with Taylor getting an edge to a searing delivery on four.
A stunned Nicholls was then out lbw after unsuccessfully reviewing the decision, before BJ Watling nervously managed to defend Cummins' hat-trick ball.
At the other end, Pattinson, playing for the injured Josh Hazlewood, was equally menacing and Latham should have gone the next over, but a diving Smith put down a slip catch he would normally hold.
Pattinson soon got his reward with a rising ball catching Watling's glove and Burns taking an easy catch to leave them at 58 for five.
New Zealand staged a mini recovery before Starc got in on the action, having Colin de Grandhomme caught in the gully for 11.
Santner was lucky to survive a review decision before scoring after he was caught off a Starc bouncer.
Australia were convinced he was out and replays showed it skimmed off the wristband of his glove, but third umpire Aleem Dar decided otherwise.
Latham brought up his 16th Test half-century before he got a thick edge to wicketkeeper Paine off Cummins, and once he was gone Australia wrapped up the tail.