Kane Williamson smashed a brilliant 48-ball 85 as New Zealand managed to reach a total of 172/4 from their quota of 20 overs.
For Australia, Josh Hazlewood took 3 for 16 while Adam Zampa got the other wicket. Earlier, Australia won the toss and skipper Aaron Finch elected to bowl against New Zealand in the T20 World Cup final at the Dubai International Stadium on Sunday.
Both teams finished second in their groups behind table toppers England and Pakistan. New Zealand edged England in the first semi-final at the Sheikh Zayed Stadium in Abu Dhabi before Australia defeated an in-form Pakistan team in the second semi-final in Dubai. While Australia lost the 2010 final to England in the Caribbean, New Zealand have reached the final for the first time.
The Kane Williamson-led side will aim to end the year with two ICC titles, having defeated India in the World Test Championship final earlier this year.