Up 21-0 at halftime, the result of New Zealanders conceding penalties and Fiji playing the ball quickly, Fiji showed form like nothing else they had produced earlier in this year's series.
The loss left New Zealand vulnerable in their hopes of claiming a semifinal berth on Sunday and dependent on Wales upsetting Fiji.
New Zealand have one more game against Kenya on Sunday which they must win to keep their slim hopes of qualifying alive.
Fiji started at speed and after Vilimoni Botitu kicked ahead and recovered the ball it was Aminiasi Tuimaba who ran around Dylan Collier from the ruck to open the scoring after a minute.
A penalty was conceded when holding into the ball in the tackle and with a quick tap the ball was moved for Sevuloni Mocenacagi to score and take Fiji out to a 14-0 lead with two minutes of the first half remaining.
The pressure was maintained by Fiji and the pain for the All Blacks Sevens was clear when from another turnover penalty Tuimaba went in again when breaking the defences open again to take them out to a 21-0 lead.
The All Blacks Sevens avoided embarrassment when the kick-off to open the second half was kicked out on the full by Vilimoni Koroi. However, Fiji made a rare error and turned the ball over, then conceded two penalties. The first gained New Zealand ground from a terrific line kick by Kurt Baker and the second resulted in their first try to Regan Ware.
Placed under defensive pressure New Zealand imploded when attempting to keep their hopes alive and poor passing resulted in the ball falling to Fiji with Waisea Nacuqu able to complete the scoring with the last try of the game.
New Zealand made a lively start to the tournament, beating Wales 54-5. They scored eight tries, the first to Tim Mikkelson after two minutes with Caleb Clarke scoring in the third and seventh minutes, Sam Dickson in the fifth, Salesi Rayasi in the sixth and 10th minutes, Etene Nanai-Seturo in the ninth minute and Regan Ware in the 11th.
Koroi kicked six conversions and Ngarohi McGarvey-Black one. Wales' only points were a try scored by Joe Goodchild in the 13th minute.
In other results, South Africa, second to New Zealand on the series standings returned to form with a 52-14 win over Argentina and a 24-12 win over France. England beat Spain 47-0 and Ireland 19-12 and the United States beat Scotland 32-14 and Japan 45-7 with their pool decider being against Australia on Sunday.