Having been sent into bat, South Africa could only muster 136 for nine in their 20 overs, a target New Zealand chased with ease for the loss of two wickets and with 22 balls to spare.
Tom Latham top-scored with an unbeaten 63 from 55 balls as he put on 96 for the first wicket with South African-born Devon Conway (39 from 26 balls) before the latter was caught in the deep by Rubin Hermann off spinner Keshav Maharaj.
It was an innings in stark contrast to South Africa, who slipped to 68 for six before George Linde (23 from 19 balls) and teenager Nqobani Mokoena (26 not out from 20 balls) brought some respectability to the total.
New Zealand shared the wickets around, with seamers Ben Sears (2-27 in 4 overs) and Lockie Ferguson (1-9 in 4) the pick.
"We lost wickets early and it's tough to recover from 46 for 5," South Africa captain Maharaj said. "But the lower order rallied to give us some runs on the board. But the batting we did in the first 10 overs really put us behind. We weren't adaptable enough and couldn't adjust.
"We are a young side, not to make excuses, but we want to take the lessons quicker. The beauty of the series is that we've still got a chance to make a comeback. We want to be more clinical with bat and ball in the next game.
"Mokoena's shots shocked us in a good way and we bowled well in parts too. He's 19, probably never dreamt of international cricket this quickly, but we are excited to see how the future looks for him. He maybe doesn't know himself how good he can be."
The fourth game in the series will be played in Wellington on Sunday. South Africa have rested the majority of their regular players with just three who featured in the recent T20 World Cup on tour.