Earlier, New Zealand scored two tries to lead their semifinal 14-0 at the break, before Fiji came storming back in the second half. They levelled the scores and sent the match to extra time, where the first score would win the game.
That came to New Zealand when Fijian-born Blues' wing David Raikuna scored a spectacular individual try to send his side through to face South Africa, who also required extra time to advance past Samoa in the other semifinal.
Yesterday, New Zealand breezed through Pool C with wins over France (21-0), Wales (40-5) and Argentina (17-5) and easily accounted for Canada (17-0) in their quarter-final.
The Kiwis are competing in the United States, the fifth stop on the circuit, without the services of DJ Forbes, Kurt Baker and Lote Raikabula, who are all out with injury.
The next stop on the circuit is the Hong Kong sevens next month.