The men will close out their first day of competition against South Africa at 10:53 a.m. ET.
The Kiwis capitalised on a yellow card to South African Rosko Specman to score tries but South Africa finished stronger and made the game safe when Tim Agaba scored in the final minute.
An early sin-binning for a New Zealand player who went high on Branco du Preez paved the way for the Boks to open a 12-0 lead with tries by captain Philip Snyman and the twinkle-toed Seabelo Senatla.
The Blitzboks made the flawless start to the defence of their HSBC World Sevens Series title by winning the season-opening tournament in Dubai on Saturday.
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.
Despite doing well to keep the ball in the second half, Shujaa finally bowed to pressure as All Blacks used the chance they got to turn over in a try that was awarded to them after a video review.More news: Tillerson will be out at State Department within weeks
The reigning series champions fell to a 14-12 defeat after a late converted try handed the Americans a shock victory.
Cape Town will host the next leg of the World Series next weekend.
"It was a long pre-season and a lot of guys went on to play some 15s so it's a new team with some unfamiliar faces".
"It's easy to play well in a team as good as this‚" Smith said.
They faced the challenge of New Zealand, who followed a 14-12 quarter-final win over Kenya by then overcoming England 14-5 in the last four.
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.