New Zealand conceded only one try in five matches leading up to the final, keeping its goalline intact in pool play and the quarter-finals, then beating England 14-5 in a tight semifinal. But Australia rocked the world champions with tries to Ed Jenkins and Paul Stannard to take an early 12-0 lead in the final, seeking its first win on home soil in 11 years and its first over New Zealand since 2011.
Curtis then scored twice as New Zealand rallied to lead 14-12 at halftime before racing away from a tiring Australian team that played 10 minutes of extra time in its semifinal.
Earlier, Australia had needed a try to Jesse Parahi in the 10th minute of extra time to beat South Africa 24-19 in its semifinal, giving it a chance to win its home leg of the World Series for the first time since 2002.
England beat a fatigued South African side 47-0 in the third-place playoff.
New Zealand beat Samoa 40-0 in the quarter-finals while England ousted Fiji 26-12, leaving the Fijians — under former England coach Ben Ryan — to take some small consolation from the plate championships.
Also, Canada finished 10th after losing 19-14 to France in extra time in the final of the Bowl, the second consolation bracket. The Canadians went 4-2 at the event, losing to Fiji in pool play and narrowly missed making the Cup quarter-finals.
In the final, Tomasi Cama, who converted both of Curtis' tries, scored and converted a try of his own to give New Zealand the comfort of a 21-12 lead and Waisake Naholo kicked ahead a loose ball to stretch the lead to 26-12.
Joe Webber scored a try that was also converted by Cama and New Zealand had scored 33 unanswered points before Australia hit back with a try to Cameron Clark.
New Zealand sealed its win, and went immediately to the top of the World Series standings, with a final try to David Raikuna.
New Zealand's Tim Mikkelson, who was the top tryscorer at the tournament with seven, limped from the field in the final and needed medical attention. Cama ended the tournament with 46 points, taking his career tally to 1,910, but Australia captain Ed Jenkins was named Player of the Tournament.
Canada got off to a strong start in its Bowl final against France, building a 7-0 lead at half-time thanks to a try from Justin Douglas of Abbotsford, B.C.
But French duo Renaud Delmas and Paul Albaladejo had gone over for tries after the break. Albaladejo converted after each try.
Replacement Sean Ferguson, also from Abbotsford, dived into the left-hand corner with just three seconds remaining in regulation time. Victoria's Connor Braid then connected with a kick to tie the game at 14-14 and force the extra time.
Julien Saubade then scored in extra time to hand France the Bowl title.
"I am very pleased and so proud of the effort, skill, attitude and commitment of the players and that includes all of them this weekend," said Geraint John, Canada's head coach. "To play like we did against the teams we faced shows great character.
"Some of these players had more game time this weekend than all of last year which shows what an outstanding effort it was."
Canada was 10th overall at last season's sevens series.