The Blitzboks now head home to South Africa for the second stop of the HSBC World Rugby Sevens Series in Cape Town on December 9 and 10.
South Africa has gotten their sevens season off to the best possible start after a dominant display in Dubai.
New Zealand typically fought back after Rosko Specman was yellow carded‚ with tries through Andrew Knewstubb and captain Scott Curry to make it a nervy end to the match.
The reigning series champions fell to a 14-12 defeat after a late converted try handed the Americans a shock victory.
"We kind of let them back into the game and a silly yellow card and one or two silly mistakes towards the end nearly cost us", Snyman said after the final.
Australia have been beaten after the final siren for the second straight match, falling to England in their Cup quarter final.
It was the flawless start to the 2017/18 season after the success of the previous year and the tonic the team needed ahead of this weekend's second tournament in Cape Town.
Jeffery Oluoch powered over from a turn over ball to put Kenya ahead, but his celebration was cut short by Seabelo Senatla, who latched onto a loose ball in the middle to draw level before he grabbed the brace for the tournament's champions.
"We deliberately didn't put the guys into anything like this in pre-season as it's such a long season for us so it was always going to be a little bit of a risk".
"It's easy to play well in a team as good as this‚" Smith said.
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.