The men's final was tied on 14 at halftime but South Africa pulled away as Olympic champions France conceded penalties and errors under pressure.
Dewald Human's grubber kick bounced kindly for Shilton van Wyk to score in the left corner, and Ricardo Duarttee converted from touch. A minute later, Van Wyk's tap and go finished with David Brits scoring in the right corner, and South Africa celebrated winning its home event on the world series for the first time since 2015.
France, which knocked out defending champion Fiji in the semifinals, started and finished the first half with tries by Celian Pouzelgues and Varian Pasquet, but in between South Africa's Donavan Don glided across and Zain Davids blew over through two Frenchmen.The USA, who were without superstar centre Ilona Maher, upset women's defending champion Australia in the semifinals 24-19 from 19-7 down with a brilliant second-half comeback inspired by Nia Toliver, who scored two tries and assisted in the third.
Toliver got the Americans' first try in the final after 25 seconds, and when Alyssa Porter pounced on a New Zealand error, they led 12-0 after two minutes.
But New Zealand dominated the rest of the way and won 26-12. Jorja Miller scored from a stolen throw-in, and Jazmin Felix-Hotham's converted try put New Zealand 14-12 ahead by halftime.
Moments after blowing a try on the line, Kelsey Teneti scored after a five-meter scrum. Dhys Faleafaga capped the scoring with an overlap try.
After losing the Dubai final to Australia last weekend, New Zealand was on top of the standings.
"We're going home with some goodies for Christmas," New Zealand captain Sarah Hirini said.