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Australia will ask New Zealand to chase a fourth-innings total of more than 450 after their bowlers had given them control of the Boxing Day Test.

Australia will ask New Zealand to pull off a seemingly impossible mission in Melbourne after Pat Cummins and their fast-bowling cartel had buried the visitors' hopes.

The Aussies went to stumps at 4-137 on Saturday's third day of the Boxing Day Test, leading the Black Caps by a mammoth 456 runs after they rolled them for just 148.

No team has successfully chased more than 418 in a Test, with the Aussies having set a similar target of 468 in Perth just a fortnight ago in their 296-run win.

Cummins took 5-28 to be the star of Saturday as New Zealand never looked like getting close to Australia's first-innings score of 467.

James Pattinson also claimed three scalps in his Test return, while Mitchell Starc's dominant summer continued with 2-30.

David Warner (38) and Marnus Labuschagne (19) fell in pursuit of quick runs, while Joe Burns was more patient in his 100-ball 38.

Steve Smith was also out again trying to pull Neil Wagner, marking the fourth time he had fallen to a short ball from the left-armer in as many innings this series.

But it was an otherwise perfect day for Australia after Cummins started the rot with the wickets of Ross Taylor and Henry Nicholls from consecutive balls.

The world's best quick bowled with great accuracy and consistency, regularly on a fourth-stump line to draw edges from the New Zealanders.

Tom Latham provided the only real resistance for the Black Caps before Cummins had him caught behind for 50, to go with his other victims Tom Blundell and Tim Southee.

Pattinson's haul of 3-34 will provide a testing time for selectors if Josh Hazlewood overcomes a hamstring strain for the final Test, starting on Friday at the SCG.

Hazlewood remains some chance of proving his fitness, but it's understood he is unlikely to be risked if Australia go to Sydney up 2-0.

After taking the prized scalp of Kane Williamson on Friday, Pattinson removed BJ Watling and Mitchell Santner on Saturday in his first Test back on home soil in almost four years.

"When you speak to guys playing (Sheffield) Shield or county cricket, they speak of him (Pattinson) as though he is one of the best bowlers in the world," Cummins said.

"We all know that - and for him to come out in front of his home fans and for everyone to see it on TV rather than in Shield cricket - great."

"That (depth) has been really prevalent in the past 12 months. We speak a lot about this group of fast bowlers that we want to keep together."

Starc also claimed two wickets to take his tally to 25 for the summer at an average of 14.60.

New Zealand must at least draw in Melbourne to keep alive their unbeaten run in Test series, which dates back to late 2017.

The task looks beyond them given they are yet to survive more than 66 overs in an innings this series.

"(Their bowling) was pretty relentless. They didn't really let us have anything," Latham said.

"The way they executed was spot on from a bowling point of view and the way we handled it was not the way we wanted to."