New Zealand sored 142/8 after winning the toss and taking first strike and then restricted their opponents to 134/9 at the HPCA Stadium. The Kiwis beat hosts India in their opening game by 47 runs.
Fast bowler Mitchell McClenaghan was the star of their neat bowling performance, taking 3/17 and derailed Australia's innings.
New Zealand picked up wickets regularly to restrict Australia from gaining enough momentum.
They needed 19 runs from the last over, bowled by Corey Anderson and then 12 from the last three balls but came up short.
Earlier, Australia recovered from a Martin Guptill (39) blitz to restrict New Zealand to 142/8.
Guptill belted 39 runs as the Kiwis powered to 58 in six overs.
But a collapse, losing three wickets for 15 runs, jolted their charge.
Guptill, skipper Kane Williamson (24) and Corey Anderson (3) all were caught in the deep while attempting big shots.
Glenn Maxwell (2/18) claimed two wickets in the slump. All-rounder James Faulkner also contributed with identical bowling figures.
The wickets kept tumbling, including two run-outs in the final over, as New Zealand's run-rate continued to drop.
Colin Munro steadied in his own style, switch-hitting throughout a knock of 23.
But Munro also handed over his wicket meekly.
Veteran batsman Ross Taylor managed only 11.
New Zealand 142/8 (Martin Guptill 39, Glenn Maxwell 2/18);
Australia 134/9 (Usman Khawaja 38, Mitchell McClenaghan 3/17)