The Kiwi women, fellow favourites Australia, France and the US had all already qualified for the knock-out stages after winning the two opening pool matches on Sunday.
Another sell-out crowd of 69,000 packed into France's national stadium to watch New Zealand, gold medallists at the Covid-delayed Tokyo Games in 2021, run out 38-7 winners over Fiji.
Tries from Jorja Miller, Stacey Waaka and Jazmin Felix-Hotham, all converted by Risi Pouri-Lane, saw them build a 21-0 lead at half-time in scorching weather.
Waaka got her second, while Manaia Nuku and Michaela Blyde also scored tries in the second period, Fiji grabbing a consolation through Adi Vani Buleki.
The result meant that Tokyo bronze medallists Fiji, who suffered a surprise 40-12 defeat by China on Monday, missed out on the quarter-finals.
China -- who made the Olympic cut after winning a repechage competition -- qualify as the second best team finishing in third spot in the three pools.
New Zealand's trans-Tasman rivals Australia, winners at the 2016 Rio Games, topped Pool B and will play Ireland in the quarters.
The match is a re-run of both sides' final pool match earlier Monday, when the Australians were made to work very hard before running out 19-14 winners.
Try machine Maddison Levi scored seven tries for Australia on Monday and crossed for another vital one as Ireland exposed chinks in the Australian armour with a high-paced attacking game.
Levi, whose sister Teagan also scored a try, was on hand with two try-saving tackles -- leaving the Australians to rethink their tactics ahead of the knock-out game.
Hosts France topped Pool C, Seraphine Okemba scoring four brilliant tries in a 31-14 victory over the United States.
The US qualified as runners-up and will play Britain, who finished second ahead of Ireland in Pool B, in the quarters.
Social media star Ilona Maher, with a strong hand-off, crossed first to hand the US the lead against France.
Kyla Cannett was then yellow carded for a high tackle, to hand France a numerical advantage.
That was made the most of immediately, the strong-running Okemba screaming into the corner for a quick brace of tries.
Okemba made it a hat-trick, Chloe Jacquet also scoring before the flyer made it an individual four-try haul in an impressive display.
The French women are looking to match their male counterparts' success, after an Antoine Dupont-inspired side claimed men's gold on Saturday, and improve on their own silver medal showing from the Tokyo Games.
