Madison Levi scored two tries as Australia took a 14-7 lead late in the first half of Sunday's decider.
But New Zealand had too much firepower from that point on, with the win firing them to the top of the standings after the seven-tournament regular season.
The Kiwis finished the regular season on 126 points, with Australia just behind on 124 and France third on 104.
Australia still have the chance to exact revenge on New Zealand - firstly in the Sevens grand final tournament in Madrid, where the top eight teams will battle it out from May 31 to June 2 to be crowned overall champions.
Then all attention will turn to the Paris Olympics, where Australia will be aiming to knock NZ off their perch.
Singapore Silver 🥈— Australia Sevens (@Aussie7s) We finish second in the league heading into the Grand Final in Madrid 🙌#Aussie7s #HSBCSVNS pic.twitter.com/fD83Pq7JMxMay 5, 2024
Australia won gold at the 2016 Olympics, but NZ were champions at the Tokyo Games.
The Australian men's team had to settle for fourth in Singapore, resulting in them finishing sixth in the regular-season standings.
Australia survived an extra-time thriller to beat South Africa 29-24 in the quarter-finals.
But they were no match for NZ in the semis, going down 28-12 despite scoring the first try of the match.
THEY'VE DONE IT 🇦🇷— HSBC SVNS (@SVNSSeries) Such an emotional reaction as Argentina and head coach Santiago Gómez Cora celebrate their nation's first ever #HSBCSVNS league title �#HSBCSVNSSGP pic.twitter.com/JPOjGMPrlkMay 5, 2024
In the bronze medal play-off, Australia were crushed 26-7 by Great Britain, with Australia's only points coming in the dying seconds.
The result sealed Great Britain the eighth and last remaining spot for the grand final tournament in Madrid.
NZ defeated Ireland 17-14 in the Singapore final.
But it was Argentina who were celebrating hardest after securing the men's regular-season title for the first time with a 14-10 win over South Africa in the fifth-placed play-off.
Argentina finished on top of the rankings with 106 points, followed by Ireland (104), NZ (93) and Australia (83).
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