Boosted by the return from injury of last season's IRB Sevens Player of the Year, Cecil Afrika, South Africa hit form to beat Australia 26-0 to top Pool C without conceding a try at Nelson Mandela Bay Stadium, the new venue for the country's sevens event.
South Africa went up against France in the last eight after also beating Canada 33-0 and Kenya 45-0.
Searching for their first tournament win of the new season, last season's overall champions and South Africa sevens title holders New Zealand ran in seven tries in each of their pool games and conceded just one - a surprise try by Morocco's Karim Abad.
But the Kiwis shut out Scotland and Dubai finalists France to reach the quarters in Port Elizabeth in imposing form after a final loss in Australia and a shock quarter-final exit in Dubai to start this season.
Frank Halai scored four tries against Scotland and crossed seven times in all to lead the tournament try-scorers list.
Fiji won 31-7 over Portugal and 42-17 over Zimbabwe but were shaken by two early Welsh tries from Tom Prydie and Richard Smith in their pool decider.
The Islanders responded with five scintillating scores, including a length-of-the-field break by Emosi Vucago, to turn the game on its head.
Samoa's victory over England effectively settled Pool A, although the Samoans were pushed all the way by the United States in their final match before scrambling the ball out of play for a 14-12 win. Samoa also beat Argentina 17-5. Against England, Paul Perez scored inside 30 seconds. Two tries by Afa Aiono and one from Faalemiga Selesele then kept Samoa out of reach, despite Mat Turner and Dan Norton pulling England back into contention.
South Africa's defence wasn't breached all day as the home team put itself on course for a quarter-final meeting with France, who knocked the South Africans out of the Dubai event at the same stage.
Newcomer Steven Hunt went over four times against Kenya in his six tries on the opening day. Afrika scored two tries on his return after missing the Dubai leg, including the crucial first against Australia on the halftime hooter in the opening day's final game.