Hosts and defending champions New Zealand recovered from an early loss to England to reach the IRB Rugby Sevens quarterfinals in Wellington on Friday.
But the second and third-ranked sides in the Sevens World Series were both knocked out on the opening day.
For the first time in its 14-year history, Fiji failed to reach the quarterfinal stage and the second-ranked side France also missed out after losing a crucial match to Argentina.
At the end of the pool stage, only Kenya, Samoa and Australia could boast 100% records, while Scotland and England reached the quarters for the first time this season.
They join South Africa, who progressed on points differential at the expense of Wales and Canada
New Zealand, who lead the world series, were beaten 19-14 by England in their opening game.
They regrouped to win their second match against Spain 36-5 and beat the United States 17-10 in the final match of the evening.
England won Group A and New Zealand also qualified for the next round.
Kenya and Argentina are first and second in Group B, while Samoa topped the Group C points table with South Africa second.
Australia and Scotland are the qualifiers from Group D.
