Australia 256 (Labuschagne 90, Henry 7-67) and 281 for 7 (Carey 98*, Marsh 80, Sears 4-90) beat New Zealand 162 (Hazlewood 5-31, Starc 3-59) and 372 (Ravindra 82, Latham 73, Cummins 4-62) by three wickets

He found calm support through Pat Cummins, who again helped Australia over the line much like he memorably did at Edgbaston in last year's Ashes. Cummins made 32 and hit the winning boundary at an increasingly gloomy Hagley Oval as the batters embraced mid-pitch.

Australia had only run down 279 or more in the fourth innings on 13 previous occasions and only twice since 2006. Only three teams in Test history had scored more runs after the fall of the fifth wicket in a successful fourth-innings chase.

The victory capped a hectic period of Test cricket for Australia, who have played 22 Tests in the last 15 months. But they will have a long breather from the format with their next assignment not until next summer against India in a five-Test blockbuster.

It was a satisfying triumph for Australia, who before this had only one won series away from home since their last Test tour of New Zealand in 2016.

But New Zealand were left bitterly disappointed as their misery against Australia continued having only beaten them once in the past three decades. With their next series against Australia not due until 2026-27, several senior players in the team might never again have a chance to beat their neighbours.

After a stirring fightback ever since being bowled out for 162 in their first innings, New Zealand had been in the box seat heading into the fourth day's play, which was delayed by an hour due to rain.

Resuming at 77 for 4 and needing a further 202 runs, Australia's hopes seemingly rested with Marsh and Head who had combined for 43 runs late on day three after a top-order collapse.

In overcast conditions, Marsh went for broke off Tim Southee's first ball when he hit a bullet to backward point only for Rachin Ravindra to drop a chance.

But New Zealand's agony was short-lived when on the next delivery Head replicated Marsh's full-blooded stroke and Will Young made no mistake at point. It completed a tough season for Head, who scored just 150 runs in 11 Test innings outside of his match-winning century against West Indies in Adelaide.

With Josh Inglis breathing down his neck, Carey's place in the team had been in the spotlight having only made two half-centuries in his previous 18 innings. Buoyed by a record-equalling 10 dismissals by an Australian wicketkeeper, Carey looked solid as he quickly moved to 19 until he was given out lbw after being trapped on the knee roll by Matt Henry bowling from around the wicket.

But Carey was saved by the DRS with ball tracking deeming the ball to be sliding down the leg side. He calmly resumed his innings and kept the runs trickling along, but did have an anxious moment on 37 when Scott Kuggeleijn loudly appealed for caught behind. New Zealand unsuccessfully reviewed as their nerves heightened.

Entering the innings on the back of consecutive ducks, Marsh rediscovered his form from the Australian summer as he and Carey notched their half-centuries and Australia reached lunch needing a further 105 runs.

A single from Marsh after the interval notched the pair's century partnership and reduced Australia's deficit to under a hundred, with batting becoming easier against the older ball. New Zealand's fading hopes seemingly rested with Henry, who was also seeking a 10-wicket haul, but Marsh continued to counterattack and whacked his bouncer for six.

Southee desperately turned to Sears and it proved a masterstroke as he trapped Marsh lbw after hitting him in front of middle and leg. Marsh reviewed in the hope that the ball was sliding down the leg side, but it was upheld in an umpire's call to spark New Zealand.

It was bedlam at a near-capacity Hagley Oval when on his next delivery Sears had Starc hitting straight to square leg. Sears almost completed his hat-trick when Cummins nervously edged in front of second slip.

But Sears was then thwarted by inventive batting from Carey and an unruffled Cummins, who continued his knack for ice-cool batting in run chases. Both batters endured some anxious moments as Southee reverted to Henry for one last push but it was in vain. Carey fell short of a deserved century as Cummins sealed victory with a punch through point and he let out a roar in celebration.