Fiji beat Wales 28-0, Spain 24-12 and Australia, winners of last weekend's Sydney tournament, 26-15.
South Africa then blew a 17-5 lead in the final as Fiji put on 17 unanswered points in the second half to claim a 24-17 victory and their first tournament win of the season.
New Zealand were second in the series standings before Hamilton with one tournament success in Cape Town after three legs.
It was heartbreaking stuff, especially for the Manu Samoa Sevens who clearly disrupted Fiji's flow for most of the match.
The hosts then hit back after Fiji twice lost the ball and an initial break from Regan Ware stretched their defence, New Zealand switched the play, and Sam Dickson scored in the corner.
A late try to captain Scott Curry has helped the All Blacks Sevens to a 19-12 win over England and a Hamilton Sevens semi-final berth.
Star playmaker Vilimoni Koroi jinked through to score New Zealand's second try, while both of England's efforts were secured by Ruaridh McConnochie.
South Africa made all the running in the first half of what was a pulsating final scoring three tries to one.
After South Africa scored the first two tries and Australia hit back on the break, Stannard had a chance to put his team in the lead but fumbled a hard low offload within metres of the open tryline.
The other quarter-final pits South Africa against Scotland.
The Challenge Trophy quarter-finals will see Wales face Canada, Argentina meet Russian Federation, the United States go up against Spain and Papua New Guinea do battle with France.
The finals will be played between the victor of the semi finals taking place between Australia and South Africa.
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