
With stops in Toulouse and London still to come, the All Blacks Sevens lead the series table with 164 points and are assured of a top four finish.
Argentina are second with 140 points and Fiji are third on 130, both sides looking likely to qualify for Paris.
In the final at the National Stadium, New Zealand raced into a 12-point lead with tries by Dylan Collier and Moses Leo.
Argentina responded, with Joaquin Pellandini going over in the corner late in the first half and German Schulz narrowing the deficit to two points just after the interval.
However, Brady Rush put New Zealand nine points up with a powerful run from his own 22.
His side clung on for victory despite Argentina cutting into the lead late on with a converted try by Marcos Moneta.
New Zealand made the final via a 19-10 semifinal dethroning of defending Singapore Sevens champions Fiji
It was New Zealand’s fourth title this season after earlier victories in Sydney, Los Angeles and Hong Kong.
Their sixth Sevens Series final this season came after a 22-10 win over Britain in the quarterfinals and a 19-10 dethroning of defending Singapore Sevens champions Fiji in the last four.
Argentina had overpowered Australia 29-12 in the quarterfinals before edging a dramatic semifinal against Samoa 24-19, with Moneta crossing over for the winning try in extra-time.
The bronze medal went to Fiji, who avenged a pool loss to Samoa by coming from 12 points down to beat their South Pacific rivals 24-19.
In the lesser finals today, Australia finished fifth after a 24-21 win over Britain while Spain were ninth and the US claimed 13th place.
France, who are fourth in the series standings, qualify automatically for the Olympics as hosts, so the battle for the final automatic spot in Paris is tight with Australia (112) and Samoa (111) separated by a single point.