They earned a place in the final by upsetting the South Africans 19-12 in their semi-final and edging England 17-12 in the quarter-finals.
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.
"You cannot win a sevens tournament on the first day, but you can lose it, and the loss to the Untied States was a wake-up call that we heeded".
New Zealand haven't won a men's title since March 2016, when they defeated South Africa in the final of the Vancouver Sevens.
In their fifth-place play-off, Fiji also scored a try in added time to secure a 19-12 win, after Tom Bowen and Dan Norton tries had hauled England back from a 12-0 half-time deficit.
Star wing Seabelo Senatla was both villain and hero against Fiji the day after he became the fastest man to 200 tries in Series history‚ achieving the feat in his 35th tournament.More news: Manhattan DA says gun law passed in Congress endangers public safety
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Blitzboks 12 - Tries: Philip Snyman, Cecil Afrika Conversion: Branco du Preez (1).
Australia fought back early in the second period with tries to Simon Kennewell and Lewis Holland reducing the deficit to 21-12 but that was as close as they got.
After going ahead against the USA through a Boyd Killingworth try, the Aussies couldn't contain Carlin Isles who snared three first half tries.
It ruined what had been a vibrant atmosphere at the superb Cape Town stadium‚ which saw thousands of fans stream to the exit after the home team's chances of winning were extinguished.
SA - Tries: Philip Snyman‚ Cecil Afrika.
Two tries from Joe Ravouvou combined with scores from Vilimoni Koroi, Tim Mikkelson, Regan Ware and Sione Molia helped the All Blacks Sevens win their first tournament of 2017 at Cape Town Stadium.