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Wednesday's wash-out at Edgbaston left defending champions Australia facing a tough battle to qualify for the semi-finals.
New Zealand, chasing 244 to win, were on 51 for two off 15 overs when rain stopped play in the Group A clash at 16:40 (SA time).
GALLERY: WAGs of the ICC Champions Trophy
Under the Duckworth/Lewis system for rain-affected matches, a minimum of 20 overs had to be bowled in the second innings for either side to win this fixture.
But at 19:25, the umpires decided no further play was possible.
The first no result of the tournament saw both sides take a point apiece.
That left New Zealand with three points after their one-wicket win over Sri Lanka and gave Australia their first point of this event after a 48-run loss to hosts England at Edgbaston last week.
Australia, already without captain Michael Clarke because of a recurrence of his longstanding back problem, suffered a fresh blow before play started when opening batsman Warner was dropped as a disciplinary measure.
Warner was left out following allegations he'd physically assaulted Root in a Birmingham bar in the early hours of Sunday morning following the defeat by England.
Adam Voges' top-scored with 71 in a total of 243 for eight with George Bailey, Australia's stand-in captain, making 55 after winning the toss.
New Zealand left-arm quick Mitchell McClenaghan took four for 65.
There was a moment of unintentional humour before play started when, during a montage of messages from team captains on the giant screens at Edgbaston, Clarke urged spectators to "drink within their boundaries".
But there was nothing funny for Australia about a collapse to 10 for two in what was a repeat of the 2009 Champions Trophy final they won in South Africa.
Shane Watson was caught behind off McClenaghan and Phillip Hughes was run out for nought by Martin Guptill, racing in from cover.
But coming in at 10 for two, Bailey -- who said Tuesday now was not the time for Australia "panic stations" -- calmly repaired the early damage.
New Zealand off-spinner Nathan McCullum (two for 46) checked Australia's progress with the wickets of Matthew Wade and Bailey.
Voges fell when he holed out off McClenaghan.
But Glenn Maxwell, brought in for Warner, added late impetus with an unbeaten 29 off just 22 balls including two sixes and a four.
The Black Caps' reply started in fine style when Luke Ronchi, a former Australia international now playing for his native New Zealand, drove Mitchell Johnson through the covers for four.
But New Zealand were soon 26 for two as Clint McKay had Guptill caught at point and Ronchi taken at gully.
Kane Williamson was 18 not out and Ross Taylor unbeaten on nine when the match was halted.
New Zealand conclude their group programme against England in Cardiff on Sunday, with Australia facing Sri Lanka at The Oval on Monday.
