They slipped to 118 ranking points, equal with South Africa, who beat Sri Lanka in Johannesburg on Saturday to go 3-0 up.

South Africa will overtake Australia if they win the remaining two matches in that series. When Kane Williamson won the toss he had no hesitation in batting first on the Hamilton wicket, correctly forecasting it would slow up as the day wore on and Boult would come into his own.

But in the prime early batting conditions, New Zealand appeared to have under-performed with their 281 for nine, despite Taylor’s 107 off 101 balls and his century partnership with Dean Brownlie who made 63.

With rankings and the series at stake after New Zealand won the first ODI by six wickets and the second was washed out, Aaron Finch and Shaun Marsh made a flying start to Australia’s reply, averaging more than six an over.

They were particularly harsh on Tim Southee, whose opening four-over spell cost 30 runs, while new-ball partner and man-of-the-match Boult then had one for 10.

Williamson and Ross Taylor, determined not to run out of time, batted at more than 6.0 an over in their 163-run third wicket partnership with New Zealand chasing down a 217-run target.

The New Zealand skipper finished unbeaten on 104 with Taylor out for 60 and Henry Nicholls not out four.

Bangladesh were in command for nearly four days, until their second innings lasted less than 58 overs to end at 160-9 and captain Mushfiqur Rahim in hospital after being felled by a Tim Southee bouncer.

It was a disappointing sequel to their imposing first innings of 595-8 declared, presenting them with the unwanted record of the highest ever score in the first innings to lose a Test.

The previous mark was set more than 120 years ago, when Australia scored 586 against England at the Sydney cricket ground in 1894.

New Zealand made a shaky start to their run chase with first innings centurion Tom Latham out for 16 and fellow opener Jeet Raval for 13, both removed by off-spinner Mehedi Hasan in the space of eight balls.

But Williamson and Taylor were unruffled on a warm Wellington afternoon that was a far cry from the blustery first day when Bangladesh batted positively on a green wicket.

Williamson brought up his century — levelling the scores with a sweep off Mehedi to the boundary — before ending the game with a single off the next ball.

Bangladesh resumed the final day at 66-3 and were in early trouble when Shakib Al Hasan, whose 217 in the first innings is a record high score for a Bangladesh batsman, lasted only five balls before going for a duck.

Mominul Haque, who has two centuries to his name in five previous innings against New Zealand, was removed this time for 23.

At 96-5, Sabbir Rahman and Mushfiqur added 18 runs in 16 overs in the face of a torrid attack from the New Zealand pace trio of Southee, Trent Boult and Neil Wagner.

Mushfiqur, who had been unable to field for Bangladesh during New Zealand’s first innings 539, was forced to duck repeatedly under a barrage of bouncers until a ball hit the back of his helmet.

He lay prone on the wicket, attended by medical staff from both teams until an ambulance drove on to the field and took him to hospital. He was later given the all-clear.

Opener Imrul Kayes, who was stretchered off and taken to hospital late on the fourth day with a hip injury, hobbled to the crease at the fall of the seventh wicket.

Unable to run, he relied on boundaries to be 36 not out when the innings ended.

Boult finished with three for 53 while Wagner and spinner Mitchell Santner took two wickets each.

The second Test starts in Christchurch Friday.

Warner smashed 119 off 115 balls to propel the Australians to an imposing 378 for five after being sent into bat. They then bowled out the Black Caps for 262 off 47.2 overs at the bat-friendly Manuka Oval.

New Zealand had to win in Canberra to keep alive their hopes of retaining the trophy after losing by 68 runs in the opening game in Sydney on Sunday.

Warner led the way in Australia’s third-highest ODI total and was supported by skipper Steve Smith’s 72 off 76 balls and Travis Head’s 57 from 32 balls, while Mitchell Marsh bludgeoned seven sixes in a unbeaten 76 off just 40 balls.

The Black Caps made a spirited attempt to chase Australia’s hefty total and were 177 for three when Jimmy Neesham fell in the 31st over for 74, ending a 125-run stand with skipper Kane Williamson.

Williamson was dismissed nine overs later for 81 off 80 balls with five fours and two sixes, and with him went New Zealand’s faint hopes of reeling in the Australian target.

Williamson’s gamble on sending the Australians into bat backfired spectacularly when the home side feasted on a perfect batting wicket.

The pugnacious Warner set the tone with his 10th ODI century — the third century in his last five ODI innings and his first against New Zealand.

Only three other Australian batsmen have scored more hundreds in ODIs — Ricky Ponting (30), Mark Waugh (18) and Adam Gilchrist (16).

“It was a fantastic wicket and once you keep wickets in hand you can make 100 runs in the last 10 overs,” Warner said.

“It was great batting with the skipper (Smith) and running between the wickets. This year is going great.” Warner was out to a low catch from Williamson at cover off medium-pacer Colin de Grandhomme in the 37th over, ending a 145-run partnership with Smith.

Smith followed up his career-best ODI score of 164 in Sydney with 72.

The Australian skipper, who was struck a painful blow in the groin by a de Grandhomme delivery on 56, sliced to Mitchell Santner at deep point.

Head hit his second half-century of the series before he was caught off Tim Southee.

Marsh provided late fireworks with some prodigious hitting, including three consecutive sixes off Matt Henry in a lusty cameo.

Smith said: “330, 340 runs was probably par. 380 was a big total. You need a lot of things to go right to chase it down.” The Black Caps lost both openers by the ninth over, with Tom Latham caught and bowled by Josh Hazlewood for four and Martin Guptill caught behind off Pat Cummins for 45.

Neesham looked in good touch with 74 off 83 balls before he was caught in the deep by Mitchell Starc off Josh Hazlewood in the 31st over.

James Faulkner got Colin Munro to hole out on 11 to long-on, where Marsh took a safe catch, and Starc had de Grandhomme caught behind for 12.

Williamson was deceived by a Pat Cummins slower ball and found Warner in the covers to leave the Black Caps on 232 for six.

Wickets tumbled among the lower order, with Cummins finishing with four for 41 as Australia cruised to victory ahead of Friday’s third and final ODI in Melbourne.

“Australia is one of the best sides in the world and at home they are the best side in the world,” Williamson said.

“The ‘death’ overs really hurt us, and Australia have been showing us how to build partnerships. “

New Zealand finished the day at SuperSport Park on 38 for three, 443 runs behind South Africa’s first innings total of 481 for eight declared.

Du Plessis made 112 not out off 234 balls and said he had stuck to a plan.

“There is a lot happening in the wicket and we just needed one guy to anchor the innings and keep them out there as long as possible,” he said.

“The plan right from the beginning was to try to get to 400, which is a good score on this wicket, and then have a little dip at them at the end of the day.”

Du Plessis said he and JP Duminy had found batting in the last hour on the first day to be particularly difficult.

His declaration was therefore geared to having New Zealand bat when it was most likely to be tough for them in South African winter conditions, with the close coming near sunset.

“The grass stands up a little more towards the end of the day and because of the light you can see the little indentations on the pitch which you don’t see when the sun is shining brightly in the middle of the day. It plays on your mind a bit.”

In an era of rapid scoring in Test cricket, much of South Africa’s innings was a return to a more attritional age, with the run rate hovering at around three an over.

Du Plessis was particularly cautious as he tiptoed to a fifth Test century off 225 balls.

But it paid off as reunited fast bowling pair Dale Steyn and Vernon Philander ripped out both openers before Ross Taylor was run out.

It left New Zealand in deep trouble in a match which will decide the series after the weather-hit, abandoned first Test in Durban.

Martin Guptill survived a sharp chance to Stiaan van Zyl at third slip off Philander when he was on four, with the ball bursting through the fielder’s hands for four more runs.

But he gave a more straightforward chance to the same fielder in Philander’s next over without adding to his score.

Steyn then had the left-handed Tom Latham caught behind off an inside edge for four, although it seemed a controversial decision. Umpire Paul Reiffel gave the batsman not out and South Africa sought a review.

It was clear that the ball had deviated off the batsman’s trousers but only the faintest flicker on the ultra-edge device gave any indication that it had touched the bat first.

But television umpire Richard Illingworth decided it was enough evidence to overturn his colleague’s decision.

Much then depended on New Zealand captain Kane Williamson and Taylor, his most experienced teammate.

Taylor was struck twice, on the shoulder and arm, by lifting deliveries from Steyn and scored only one before pushing a ball from Kagiso Rabada to midwicket. He set off for a run, was sent back by Williamson and was beaten by a direct hit from Temba Bavuma.

Pretoria-born Neil Wagner was New Zealand’s most successful bowler, taking five for 86.

“Neil’s been outstanding for a long period of time,” said fellow fast bowler Tim Southee.

“He’s just reaping the rewards for the efforts and the tough overs he’s bowled throughout his career. He keeps running in and will make something happen from nothing.”

Southee collected a solitary wicket and conceded 114 runs.

“It was frustrating,” he admitted. “When the ball did something it did too much, but credit to the way South Africa batted, particularly Faf.”

The Proteas can nudge up one place to sixth in the International Cricket Council (ICC) Test rankings if they win, while the Black Caps will remain fifth irrespective of the result.

But the reputation of Test cricket is at much at stake as rankings points after a farcical first Test in Durban where less than 100 overs of cricket were played before a wet, soft outfield prevented any play on the last three days. There was even less cricket in a Test match between the West Indies and India in Port of Spain, also because of outfield conditions.

It is the first time Test cricket has been played in South Africa in August, almost two months before the usual start of the season.

Preparing grounds for winter conditions has been a challenge – which Durban failed to meet after re-seeding the outfield only two months before the match. Following reports from the match referees, the outfields in Durban and Port of Spain were condemned as “poor” by the ICC.

Centurion groundsman Rudolph du Preez had the advantage of planting winter grass much earlier than Durban, with work starting in April, almost immediately after the 2015-16 season.

He said it was necessary to plant winter grass because fielders struggled on dry, dormant summer grass when the same two countries met in a one-day international in August last year.

With virtually no rain falling on the South African Highveld during winter – and no rain predicted during the Test – Du Preez is confident that conditions will be suitable for Test cricket. He said more time had been necessary to prepare the pitch because cool conditions meant it took longer to dry out after watering.

Du Preez said he did not expect uneven bounce to be as much of a factor as it has been in the later stages of matches in recent seasons.

“It might not deteriorate as we are used to. It might be a little bit slower, it might be holding back a bit more,” he said. Centurion has been a fortress for South Africa in Test cricket, with the home side having won 16 of the 21 Tests at the ground. Their only two losses were against England in a contrived result in 1999-2000, engineered by the late Hansie Cronje before he was banned from cricket because of his association with bookmakers, and against Australia in 2013-14.

South Africa: Faf du Plessis (capt), Dean Elgar, Stephen Cook, Hashim Amla, JP Duminy, Temba Bavuma, Quinton de Kock (wkt), Vernon Philander, Kagiso Rabada, Dale Steyn, Dane Piedt

New Zealand: Kane Williamson (capt), Martin Guptill, Tom Latham, Ross Taylor, Henry Nicholls, BJ Watling (wkt), Mitchell Santner, Doug Bracewell, Neil Wagner, Tim Southee, Trent Boult