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Conceding two late tries in both halves, the All Blacks Sevens paid for numerous mistakes which were pounced on by the unbeaten tournament hosts.
It means New Zealand won't repeat their win from the previous tournament in Cape Town and will lose their overall series lead to South Africa.
Clark Laidlaw's team had vowed to bounce back from a tense 19-17 pool loss to Fiji late on day two but they produced their worst performance of the tournament.
Trailing 12-7 at halftime, Vilimoni Koroi's second try levelled the score and gave New Zealand momentum.
However, the hosts surged home through tries to Maurice Longbottom and captain Lewis Holland.
Dynamic playmaker Koroi was exceptional for New Zealand but didn't have enough support throughout the three-day tournament.
The brief bench appearances of former rugby league age group star Etene Nanai- Seturo suggested a bright future for the 18-year-old.
Chasing their first world series title since 2012, Australia's semi-final opponents will be unbeaten Argentina, who shut out England 10-0.
Earlier, series defending champions South Africa charged into the last four with a 17-0 whitewash of Kenya.
They will meet the United States, who toppled Olympic champions Fiji 24-7.