Carey and Mitch Marsh, who made 80, did the business for Australia, who stumbled to 4-34 before reaching their 279-run fourth-innings target to win by three wickets.

The off-the-canvas performance means Australia's dominance over New Zealand at Test level will extend into a fourth decade.

Not since 1994 have the Black Caps held the Trans-Tasman Trophy, with Australia now enjoying ownership until their next battle in Australia over the 2026-27 summer.

Carey was an unlikely match-winner for Australia, with just 27 runs to his name in three previous innings in New Zealand.

As some pondered whether he might fight off the challenge from Josh Inglis to keep his spot beyond the series, the South Australian played with poise and determination to carry his country over the line.

"I enjoy that challenge," Carey said of the scrutiny.

"This group's been able to get out of situations.

"At times (we've been) a bit under pressure, but we've stayed resilient throughout that and believed ... everyone's had their moments and it's a really special team to play in."

Marsh and Carey combined at 5-80, after the loss of Travis Head, to put on 140 runs together - the biggest partnership of the series, when the pressure was at its heaviest.

New Zealand pace debutant Ben Sears (4-90) gave Australia a mighty shake, removing Marsh and then Mitchell Starc in sucessive balls to reduce the tourists to 7-220.

After Pat Cummins survived the hat-trick ball, the captain played a steady hand alongside his wicketkeeper, steering Australia to victory in their last outing of the summer.

Cummins robbed Carey of a century, making 32 off 44 including the winning runs with a boundary through point.

"I was happy with that. I didn't want to get on strike again," Carey said.

"It was pretty tense," Cummins agreed.

"But an amazing win. Bit by bit the boys were fantastic today."

Cummins' presence to the end evoked memories of the first Ashes Test last year, when Australia scored 8-282 to win at Edgbaston.

While Australia's fight at Hagley Oval must be applauded, the win itself was more of a bits-and-pieces victory after several batting failures.

On a nervy day on the South Island, the Kiwi bowlers were unable to cash in when play began after an hour-long rain delay.

Matt Henry - named man of the series after 17 wickets in two Tests - wasn't able to add to his haul, with Tim Southee the most dangerous bowler early.

Marsh and Head offered chances in Southee's first over of the day, both cutting straight to point a ball apart.

Rachin Ravindra had dropped a dolly to give Marsh a reprieve and a run; a nightmare put-down and a turning point for the match.

Will Young made no mistake when Head offered a carbon-copy shot for a left-hander on the next delivery.

Ravindra's blunder was a reminder of the gulf in fielding skill: the Black Caps dropped nine chances across the two Tests.

Marsh and Carey's century stand wasn't chanceless: Marsh almost played on from Southee's bowling, and Carey fell the right side of two reviews.

But under lights, Glenn Phillips, Southee and Henry probed in hope of an eighth wicket without the next breakthrough.

"This morning was always going to be a crucial period," Southee said.

"We saw it beat the bat a few times but they were able to weather that storm,"

New Zealand's defeat came despite a mighty third innings of 372 which erased a 94-run first innings deficit and set a target of 279.

Australian Associated Press