Fiji downed their Kiwi rivals 24-12 and won the pool on points scored, but also slipped to a surprise 21-19 loss to Scotland at Nelson Mandela Bay Stadium.
Earlier, New Zealand beat Scotland 14-7 and ran all over England to trounce them 24-7.
New Zealand have won the last three South African titles and are looking to become the first team to win the same leg of the Sevens World Series for a fourth consecutive time. They have, however, lost in both finals so far this season.
No other team has achieved this since the tournament started in 1999.
Host nation South Africa took a perfect record to the quarter-finals with triumphs over Samoa (29-7), France (12-5) and Australia (17-7) to qualify top of Pool A, and will face the US in Sunday’s quarter-finals while France progressed in second spot and will play Portugal. Dubai and Samoa missed out.
Wales and Argentina progressed from Pool C, dumping out Kenya despite all three finishing with seven points, as Wales pulled a decisive 33-14 victory over the East African team. Last-placed Spain finished on a measly three points.
In Pool D, Portugal and the US were successful, as Portugal matched South Africa’s unbeaten pool tally of nine points. Canada and Zimbabwe did not progress.
In the knockout stage South Africa goes up against the US, New Zealand is set to play Wales, while Fiji goes head to head with Argentina and Portugal clashes with France.
The competition in South Africa is the third leg of the 2012-13 World Series.
Samoa 12-7 France (Pool A)
South Africa 17-7 Australia (Pool A)
Kenya 14-33 Wales (Pool C)
New Zealand 12-24 Fiji (Pool B)
Portugal 28-7 Canada (Pool D)
US 21-17 Zimbabwe (Pool D)
Argentina 21-14 Spain (Pool C)
Scotland 12-33 England (Pool B)
France 5-12 South Africa (Pool A)
Samoa 7-26 Australia (Pool A)
Canada 12-26 US (Pool D)
Portugal 17-12 Zimbabwe (Pool D)
Wales 7-12 Argentina (Pool C)
Kenya 26-14 Spain (Pool C)
Fiji 19-21 Scotland (Pool B)
New Zealand 24-7 England (Pool B)
France 31-5 Australia (Pool A)
Samoa 7-29 South Africa (Pool A)