Substitute Gayle Broughton fired New Zealand back in front when she stepped inside two United States defenders before storming 80m to score under the posts straight after halftime.
During the final in the weekend, the Black Ferns beat France 29-0.
Michaela Blyde stole the show with a hattrick - ending the tournament with nine tries in total - while Portia Woodman and Tyler Nathan-Wong also got on the scoresheet in what proved to be a comfortable victory.
They finished seventh overall. We want this team to create its own history and legacy.
Sione Molia scored two of New Zealand's five tries in the men's final, while Joe Ravouvou also scored one to solidify his spot as the tournament's joint leading tryscorer, before being named tournament MVP.
John Dalziel's side fought back from 26-0 down to win 31-26, with Jamie Farndale scoring the match-winning try in the last play of the game.
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Men's action is scheduled to conclude on Sunday (July 22).
"We've worked it well and the players have delivered what they needed to today", Baber added. Fiji will play defending World Champions New Zealand, who edged France 12-7. "We managed to find a way to win", said New Zealand coach Clark Laidlaw.
A Samoan yellow card for a high tackle handed England a momentum shift, and they took advantage of the extra man immediately, spreading the ball the width of the pitch where Mike Ellery ghosted his opposite man to dot down for England's second score - Mitchell's extras made it 12-5 at half-time.
Unlike England and Scotland, Wales and Ireland were not seeded straight into round one, and faced games against Zimbabwe and Chile respectively to make it into the round of 16.
Portia Woodman, the top scorer on the worldwide sevens circuit this season with 43 tries, opened her World Cup account with a brace of tries in a one-sided 57-0 rout of Mexico at AT&T Park.
SA Points' scorer's v Ireland - Tries: Siviwe Soyizwapi (4), Justin Geduld (2), Werner Kok.
1 killed, 13 injured in shooting in Toronto, gunman dead
Toronto Mayor John Tory told reporters that the city has a gun problem and guns were too readily available to too many people. John Tulloch said he and his brother had just gotten out of their auto on Danforth when he heard about 20 to 30 gunshots.