Just on halftime, Afrika was sinbinned and New Zealand capitalised through Joe Webber, the last, inside, pass delivered by Stowers. New Zealand was back in the contest at 10-12 at the break, but there was a feeling they were just hanging on as the energised South Africans tackled like demons and hammered them at the breakdown.
Seabelo Senatla's sheer pace gave South Africa a nine point margin, which was pulled back to two when Webber's nice right foot step saw him go between the uprights.
South Africa, however, were not to be denied, and Kwagga Smith sealed it with two minutes to play.
Earlier, New Zealand had dispatched USA 28-7 in the quarter-final, with a Sam Dickson double, and Argentina 29-0 in the semifinal. Australia beat Argentina 34-19 to clinch third position.
The consolation for New Zealand is that they rise up the table to third place on 47 points, one clear of Australia. South Africa take the lead on 59 from Fiji (51). The next leg of the world series is the annual sevens jamboree in Wellington on February 6-7.