Fiji were on the back foot 30 seconds into the game when Josua Vakurunabili was yellow carded and during his absence Kwagga Smith scored the opening try for South Africa.
It's the 2016 Olympic gold-medallists' first World Sevens Series event triumph of the season, and their first win on Kiwi soil since 2010.
The Blitzboks were in commanding form throughout the tournament, as they had been in Sydney a week earlier.
Australia finished third after beating New Zealand 8-7 in the Bronze Final with a dramatic penalty drop goal after the final siren.
An unrelenting Fiji have secured Hamilton Sevens glory against all the odds, rallying from a 17-5 half-time deficit to beat red-hot favourites South Africa 24-17 in Sunday's final.
RUBY NYIKA STUFF Brothers Luke left and Jamie Wenman travelled to Hamilton from Palmerston North for Luke's sevens stag
The side had started the day on a poor footing, losing 33-12 to Sidney Sevens champions Australia in the Cup quarters, but managed to bounce off with a neat 33-19 win over Scotland in the fifth place semi-final.
Wales Sevens head coach Gareth Williams believes his young team needs to continue riding the learning curve after the weekend's World Series action in Hamilton, New Zealand. "We had an opportunity to score and did not, they countered and scored and then got the momentum", Powel said.
It was sweet revenge for Samoa, who had lost 19-14 to Kenya in their Group D encounter on Saturday.
Wales scored another two tries in the second half to just the one from Russian Federation to win 33-7 in the end.
England were over inside the first minute again against Papua New Guinea as Tom Bowen raced away to dot down within the first 60 seconds, in the first of what turned into a hat-trick against the Pacific Islanders in a 27-0 victory.
Four minutes later, Naduva, the man in the only green boots in the final, ran around the Blitzboke defence to level scores 5-all.
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