Chasing 279 for victory, Matt Henry and debutant Ben Sears ripped through the Australian top order at Hagley Oval on Sunday, leaving Australia dazed at 4-34.

Travis Head and Mitch Marsh survived an onslaught through to stumps, but at 4-77 and with 202 remaining for victory, Australia have it all to do.

New Zealand flipped the script on decades of Australian trans-Tasman Test dominance on day three in Christchurch, cashing in on a day that held rich promise.

Resuming at 2-134 and just 40 ahead, the Black Caps knew a strong second innings total could set them up for their first home Test win over Australia in 31 years.

Rachin Ravindra (82) and Daryl Mitchell (58) tallied half-centuries to set the tone, joining Tom Latham (73) and Kane Williamson (51) who posted fifties on Saturday.

Even Scott Kuggeleijn made a contribution with the bat, slogging 44 off 49 to frustrate the Australian attack.

New Zealand's final total of 372 was more than double each of their previous efforts with the bat through the two-Test series.

Australia bowled without penetration on a wicket which seemed to improve with every session.

In search of answers, Pat Cummins offered eight of his XI the chance to bowl - even Marnus Labuschagne, who earned a Bronx cheer after a rank short-pitched wide with his first ball.

Cummins led the way with 4-62, including the wickets of Williamson, Ravindra and Latham.

Nathan Lyon (3-49) joined the party late, taking three of the final four wickets.

Most New Zealand dismissals came from edges, with Alex Carey equalling an Australian all-time record with 10 catches behind the stumps.

Ravindra drove New Zealand forward, beginning on 11 and ticking the Kiwi lead into triple figures by dancing down the wicket and slogging Lyon to the long-on boundary.

Upping his scoring rate, the 24-year-old notched his half-century with a straight drive off Mitch Marsh.

Ravindra faced criticism for two ordinary first-innings dismissals this series, but in both Tests has rebounded with second-innings 50s.

He combined with Mitchell for a series-best 123-run stand which had New Zealand sitting pretty at 3-278.

Both were caught behind soon after Australia took the new ball.

Tom Blundell (9) followed when Marnus Labuschagne dived well at cover, but the Australian No.3 then dropped Kuggeleijn in the slips when he was on two.

Kuggeleijn and Glenn Phillips added another half-century partnership, heightening Australia's task.

If the flattened pitch offered hope to the Australian bats, Henry and Sears soon extinguished it.

Following his first innings 7-67, Henry was unplayable at times in a nine-over spell from the Botanical Gardens end, claiming both openers.

The 32-year-old trapped Steve Smith (9) plumb in front, while Usman Khawaja (11) was brilliantly caught by Southee at third slip.

Debutant Sears had Labuschagne (6) caught-and-bowled off a leading edge, two balls after Mitchell dropped a sharp chance at second slip.

Cameron Green (5) was beaten for pace by Sears and played on.

While Marsh and Head steadied the ship, Australia remain a long way from home.

Lyon said Australia still had belief given their depth of batting.

"We've got all confidence and all belief," he said. "Anything is possible."

Defeat for Australia would mean a second-straight drawn series, after their home disappointment against the West Indies.

For New Zealand, it would salvage the series at 1-1, and bring a home victory a generation of Kiwis are yet to taste.

"It would be a great feat," Latham said.

"If that comes tomorrow, fantastic, but ... for us it's about taking each ball at a time tomorrow."

Wr

Australian Associated Press