Warner smashed 119 off 115 balls to lead a bevy of big scores by the Australians at the bat-friendly Manuka Oval.
The Black Caps must win to keep alive their hopes of retaining the trophy after losing by 68 runs in Sydney on Sunday.
But New Zealand skipper Kane Williamson's gamble to send the Australians into bat back-fired spectacularly when the home side feasted on a perfect batting wicket.
The pugnacious Warner raised his 10th ODI century off 101 balls to continue his outstanding form with the white ball.
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It was his third ton 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).
Smith followed up his career highest 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 when he was on top of the New Zealand bowlers.
Head hit his second half-century of the series before he was caught off Tim Southee.
Aaron Finch, dropped two balls before by wicketkeeper BJ Watling, was bowled attempting to sweep spinner Santner for 19 in the 13th over, ending a 68-run opening stand with Warner.
New Zealand brought back experienced paceman Southee for Lockie Ferguson.
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