Ahead 14-7 at half-time, the Kiwis ran in four second-half tries to seal the win.
Joe Ravouvou scored a try in each half, with Vilimoni Koroi, Tim Mikkelson and Regan Ware also crossing before Sione Molia wrapped up proceedings deep into added time.
The New Zealanders, who lost to South Africa in last week’s Dubai final, hadn’t won a world series final since their victory in Vancouver in 2016.
It’s their first win under new coach Clark Laidlaw, and puts them top of the 10-tournament ladder, two points clear of last year’s series winners South Africa.
New Zealand shocked world series champions and hosts South Africa 19-12 in the Cup semi-finals after edging England 17-12 in the quarters.
Despite a worrying pool play hiccup against the United States, New Zealand advanced to quarters yesterday.
They bounced back to trounce Spain 50-0 in their second match, running in eight tries, including braces to Tim Mikkelson and Sam Dickson, then went on to beat Australia 35-12.
A loss to Australia would have resulted in the Kiwis missing out on the top eight for the first time 20 years, but a dominant first half meant that was never really likely.
Vilimoni Koroi’s opening try was supplemented by a double from Dylan Collier for a 21-0 half-time lead, although Australia hit back early in the second spell through Simon Kennewell and Lewis Holland.
However, closing tries to Koroi and Sione Molia sealed the match comfortably for New Zealand.
New Zealand coach Clark Laidlaw said it had been pleasing to see his team recover after their opening loss.
“We were pretty poor against the USA but we’re really happy about the way we bounced back,” he said.
“You can’t win the tournament on day one but you can definitely lose it.”
The All Blacks Sevens made an encouraging start to the 10-leg circuit last week in Dubai, beaten 24-12 by South Africa in the final.
The home side rebounded from their lose to New Zealand to defeat Canada 19-17 to claim bronze.
Fiji defeated the United States to finish in fifth, while Australia claimed the Challenge Trophy by defeating Spain.
Joe Ravouvou was named player of the final, and scored six tries over the two-day tournament.
Sydney will host the next leg of the world series, in January 2018.