Throughout the day as the contest played out on a relatively mild fourth-day pitch, both sides had moments when they took control. But it was Marsh's innings of 80 and Carey's steady hand which guided Australia to victory.

Its total of 281-7 completed the 14th-highest successful fourth innings run chase in test history.

On the other side, New Zealand narrowly missed out on its first test win over Australia in New Zealand in 31 years. Its last win in Australia came in Hobart 13 years ago.

When Marsh was out, Australia needed 59 runs with four wickets in hand and when Mitchell Starc was out next ball, it needed 59 with three wickets and the match turned briefly in New Zealand's favor.

But Carey kept Australia on track and added another 61 unbeaten runs with captain Pat Cummins who hit a four through cover for the winning runs and finished 32 not out.

Carey had strike on 97 with three runs needed and a chance to complete his century which would have been the first century of the match. But he gloved a single and Cummins ended the run chase a few balls later.

"I was happy with that," Carey said.

"I didn't want to be on strike again. It was a great series and this match ebbed and flowed. We had our backs against the wall this morning, they came out and put us under the pump so it's nice to chase those runs down."

Australia started the fourth day one hour late after a heavy shower at 77-4 needing 202 runs to win the match while New Zealand needed six wickets. The tension in that scenario once again demonstrated the enduring fascination of the five-day game.

Rachin Ravindra dropped Marsh at point from the first ball of the second over of the day bowled by Tim Southee. Marsh was 28. On reflection, that may have been the moment New Zealand lost the game.

Overnight batsman Travis Head was out next ball, caught by Will Young at point off Southee, but Marsh's wicket was the critical one and when it escaped New Zealand there was a change in the match.

Marsh and Carey simply tried to bend the match to their will from then on. Both reached half centuries before lunch, Marsh from 54 balls and Carely from 60. Together they helped Australia add 97 runs from 19 overs in the morning session at rate of more than five runs per over.

Their innings were more impressive in context: both were under some pressure when they came to the crease. Marsh had been out for ducks in his two previous innings and Carey had scores of 31, 0 and 14 in his previous innings in the series. Both batters dug deep to find the strength to defy New Zealand's push for victory.

By lunch Australia needed 105 runs to win with five wickets in hand and the balance of the match tipped in its favor. As Marsh and Carey continued, the odds against New Zealand lengthened.

"I thought Mitch Marsh's intent was outstanding and got us going a little bit," Carey said.

"That was the messaging this morning. Let's go out there and play our way and if you see an opportunity, take it."

Young fast bowler Ben Sears, on Test debut, finally broke the partnership in the first hour of the second session. New Zealand appealed for lbw when the ball struck Marsh in front of leg stump and the on-field umpire upheld the appeal.

The replay showed the ball just nicking leg stump and that was enough to send Marsh on his way.

New Zealand had had no success with reviews in the morning when Carey overturned an lbw decision and survived an appeal for caught behind.

Australia had a 94-run lead on the first innings when it made 256 after bowling New Zealand out for 162. Marnus Labuschagne made 90.

New Zealand made 372 in its second innings for an overall lead of 279. That looked substantial when Australia was 34-4 and 80-5 but ultimately it proved inadequate.

"It ended up being a great Test match," New Zealand captain Tim Southee said.

"Obviously the partnership with Mitch Marsh and Alex Carey broke the back of our attack, but it was a great little end to the day."