The 20-year-old Metuisela Talebula scored one of six tries for Fiji at Twickenham and converted the others as New Zealand failed to reach the cup final for just the third time in eight events this season.
But its performance was still enough to secure an unassailable lead over England in the overall standings.
England was the only team able to stop New Zealand hoisting the title going into Sunday's second day of the London Sevens but the tournament host lost 19-17 to Kenya in the bowl quarterfinals before rebounding to win the shield final with a 22-7 win over Portugal.
South Africa ended the Fijians' run in the cup final, winning 24-14 to add the London title to the USA Sevens honor it won in February.
Having ended Australia's defense of the London title in the quarterfinals and beaten Rugby World Cup Sevens champion Wales 21-19 in the semifinals, South Africa outscored Fiji by four tries to two, with Bernado Botha touching down twice.
Samoa's Tom Iosefo finished as the tournament's leading try scorer with 10 after scoring two in a 22-12 win over Australia in the plate final, while Scotland edged Kenya 21-19 to take the bowl.
