Opener Connor Esterhuizen anchored the South Africa reply with an unbeaten 45 from 48 balls as the Proteas won with 20 balls to spare in Mount Maunganui on Sunday.
He was supported by Dian Forrester, also on debut, who stayed with him for more than six overs and finished 16 not out.
Esterhuizen finished the chase with a six off Kyle Jamieson from the fourth ball of the 17th over.
New Zealand's spinners helped to make a fight of it, captain Mitchell Santner taking 1-8 from his four overs on a turning pitch at Bay Oval.
"I think all the plans paid off and the execution was top-notch from our bowlers," said South Africa captain Keshav Maharaj, who took 2-25 off his four overs.
"It was a young bowling line-up, but whatever we asked them to do, they stood up.
"It was a little nervy towards the end but it showed the maturity in Connor and Dian in the way they played to take it over the line."
New Zealand had eight players missing from their World Cup squad, including their top six batters from the team that lost the final against India by 96 runs after beating South Africa by nine wickets in the semi-finals.
After choosing to bat first, New Zealand lost five wickets in the powerplay, couldn't recover and stumbled to their 10th-lowest score in T20 internationals, and their second-lowest against South Africa.
Gerald Coetzee dismissed New Zealand openers Devon Conway and Tom Latham within the first three overs, finishing with 2-14, then Ottneil Baartman took 2-22 to help complete the ruin of the New Zealand top order.
Man of the match Nqobani Mokoena ran through New Zealand's lower order, taking 3-26 to stifle any hope of a late resurgence.
19°C