PHOTO: AFP
After Warner's dismissal, Australia were still 90 runs short of their target with an unbeaten 69 from Mitchell Marsh and John Hastings not out 48, getting them over the line.
Warner was nudging his sixth ODI century when he was undone by New Zealand's match ace Mitchell Santner, but by then he had done enough to ensure the world champions were in a dominant position.
Australia lost six wickets as they chased down New Zealand's 281-9 with 21 balls to spare.
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After New Zealand won the first match by 159 runs the series will now go to a decider in Hamilton on Monday.
Both sides suffered middle-order batting blues, but Australia had better padding with Warner and Usman Khawaja in a 122-run opening stand.
Warner's 98 came off 79 deliveries and included eight fours and four sixes, while Khawaja batted at a run-a-ball for his 50.
They made it clear at the start of the innings they would attack New Zealand's strike bowlers Trent Boult and Matt Henry.
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Khawaja hit the first and fourth balls he faced in Boult's opening over to the boundary while at the other end, Warner also smacked Henry's first delivery for four.
By the end of the sixth over Australia had 50 on the board and Boult and Henry were pulled from the attack.
Brendon McCullum worked through a range of bowling options to upset the batsmen and was eventually rewarded when Santner had Khawaja caught and bowled.
The breakthrough signalled a return for Henry and Boult. Henry removed Steve Smith and George Bailey with successive deliveries and Boult claimed Glenn Maxwell as Australia lost four wickets for 22 runs.
Mitchell Marsh joined Warner to stop the slide and they added 47 for the fifth wicket before McCullum turned once more to Santner and was again rewarded by the left-arm spinner who had Warner lbw.
It was originally given not out, but New Zealand's appeal proved successful when the ball-tracker technology showed the delivery would have hit the middle stump.
It continued Warner's bad run of luck with lbws after he was given out in the first ODI and did not appeal when subsequent reviews showed that dismissal would have been overturned.
Matthew Wade went for a cheap two when Adam Milne leapt to take a one-handed catch on the mid-wicket boundary to give Santner his third wicket.
New Zealand's 281 owed much to Santner and his tail-end partnership with Milne as well as Kane Williamson's 60.
McCullum produced his trademark onslaught to get a brisk start and New Zealand reached 35 in the fifth over when he was bowled by Scott Boland for 28.
But the rest of New Zealand's top order were unable to maintain momentum and even Williamson's 60 took 74 balls.
At the start of the 30th over, New Zealand were 152-3. Just over 11 overs later they had added only 53 runs and critically lost four wickets to be 205-7.
Santner, known as "Flatline" for his unflappable nature, stepped up with an unbeaten 45 and a 61-run partnership with Milne who made 36 off 27.
Josh Hazlewood took three for 61 while Adam Zampa, on debut, Scott Boland and Marsh took two wickets each.
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