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The opener was caught behind off the first ball of the innings in an ominous start to Australia's run chase after the Black Caps posted a competitive 7-158 overnight on Monday.
Indeed Australia looked in trouble after losing 3-1 - including the prized scalps of Steve Smith (35) and Marcus Stoinis (28) - to slump to 6-115 in the 16th over.
But after Ashton Agar (23) was dismissed with Australia needing eight runs to win off three balls, Josh Inglis coolly stepped up to thrash Kyle Jamieson for consecutive fours and ice a morale boosting win with a delivery to spare.
There will still be concern for Warner ahead of Australia's opening World Cup clash with South Africa on Saturday night.
He has had little time in the middle since being dumped as captain of Indian Premier League outfit Sunrisers Hyderabad and then left out of the team completely after two failures when the tournament resumed last month.
He lasted just one ball, sensationally caught in the slips by a diving Martin Guptill off Tim Southee.
Captain Aaron Finch hit 24 off 19 while Mitch Marsh thrashed 24 off 15 to lead a recovery before Smith and Stoinis shared a 48-run fourth wicket stand.
Mitchell Santner (3-22) took two wickets in an over, combining with Trent Boult (2-13) to spark Australia's mini-collapse before Agar and Mitchell Starc (13 not out) hit back, ensuring they needed 13 to win off the final over.
Australia claimed a rare T20 victory without using Glenn Maxwell, Pat Cummins, Mitch Swepson and Josh Hazlewood.
Australia - who play another warm-up against India on Wednesday - have fallen from top spot to seventh in the T20 rankings with just six wins from their past 21 games.
Earlier, leggie Adam Zampa (2-17) and quick Kane Richardson (3-24) did their best to restrict New Zealand after Australia won the toss.
Zampa removed Guptill (30 off 20 balls) and captain Kane Williamson (37 off 30).
Richardson also provided coach Justin Langer food for thought ahead of their tournament opener by claiming the last three scalps including two in the final over.
The Black Caps got off to a flyer thanks to Guptill and fellow opener Daryl Mitchell, who retired on 33 not out off 22 balls.
Mitchell took a liking to Mitch Marsh (0-53 off four overs), hitting three fours and a six in an over that cost the Aussie 25 runs.
Late hitting from James Neesham (31 off 18 balls) ensured a competitive target.