With his most experienced side ever, head coach Neil Powell notched up his fifth tournament win of 2017 and continued South Africa's dominance on the global stage.
South Africa has gotten their sevens season off to the best possible start after a dominant display in Dubai.
Tries from Andrew Knewstubb and Scott Curry brought New Zealand back into the match in the second period.
The Blitzboks made the ideal start to the defence of their HSBC World Sevens Series title by winning the season-opening tournament in Dubai on Saturday.
Eden Agero put restored Kenya's lead thanks to some quick thinking as he rose off the ruck unnoticed after tapping against the ball and then racing clear of two Ugandan clutches score to make it 12-7. A try in the last few seconds from Tim Agaba, however, sealed the 24-12 victory for the Blitzboks.
"We kind of let them back into the game", said Snyman.
Points from the first two tournaments of the series will be added to teams' totals in 2016-17 to determine seedings at the Rugby World Cup Sevens in San Francisco next July.
Remarkably, it was just the third time in their history that the New Zealand women's sevens have been knocked out before the semifinals, having been defeated by Australia and England in quarter-finals in 2015.
"We're also really pleased with some of the young guys who played today like Harry Glover who was fantastic and showed some great glimpses as well as Ben Howard who made his World Series debut today - we saw some really good stuff from him".
On day one the Blitzboks topped Pool A with emphatic wins over Kenya (48-5) and Canada (28-0) while battling to a rusty 19-10 win over Uganda in their opening game of the tournament.