The All Blacks have been much maligned heading into their third consecutive title defence but they floored the Boks with 17 points in just five first-half minutes to silence their critics.
It was the culmination of a thrilling first full day of action at the tournament in Japan after Australia came from behind to beat Fiji 39-21, and France scraped past Argentina 23-21.
"Today was a big game for both sides and fortunately for us, we came out on top," said All Blacks coach Steve Hansen.
"It was another titanic struggle between New Zealand and South Africa and hopefully the people watching here today enjoyed it and got excited by it."
In Yokohama, the venue for the final on November 2, New Zealand went behind to an early penalty but they turned the game on its head to take the game in a 23-12 win.
- Scrappy Australia beat Fiji -
Australia hooker Tolu Latu scored two tries in five minutes as the Wallabies came from nine points down in the second half to beat Fiji 39-21 and escape a huge upset at the Rugby World Cup on Saturday (September 21).
Fiji haven't beaten Australia for 65 years - a run of 17 winless games against the two-time world champions - whose fans dominated the crowd of 36,482 at the indoor Sapporo Dome.
But that did not stop a physical team featuring several of Fiji's Olympic Sevens gold medallists going ahead 21-12 against the 2015 runners-up four minutes after half-time.
Australia, rattled by Fiji's powerful running, eventually made their forward dominance count thanks to unlikely try hero Latu's double following the match-changing entry of scrum-half Will Genia.
- Low-key England beat Tonga in opener -
Former champions England laboured to a bonus-point win against lowly Tonga in their opening Rugby World Cup match on Sunday (September 22).
Eddie Jones' side were left to rue a series of handling errors under the roof at the Sapporo Stadium and they only secured the vital bonus point for four tries with three minutes left on the clock, running out 35-3 winners.
A full-strength England side, seen as one of the sides to beat at this year's World Cup, took their time to get going against the physical Pacific islanders and were indebted to rampaging outside centre Manu Tuilagi for two first-half tries.
- Ireland make mince-meat of Scotland -
In Sunday's (September 22) marquee fixture, a dominant display by Ireland's forwards earned them an impressive bonus-point win over their Celtic rivals Scotland.
The emphatic 27-3 victory underscored their status as one of the pre-tournament favourites.
World Player of the Year Johnny Sexton answered his critics after a worrying dip in form as Ireland shrugged off injuries to key players in their back line to seize the initiative in a tight group.
But it was the tight five forwards who broke Scotland's resistance, with pushover tries in the first half from lock James Ryan, prop Tadhg Furlong and hooker Rory Best.
Scotland had lost six of the previous seven games against the Irish but scented an upset in Yokohama as coach Gregor Townsend named the most experienced Test team in Scottish rugby history with an astounding 630 caps in the starting XV.
Rest of the scores:
POOL A: Japan 30 - 10 Russia (Friday, September 20)
POOL A: France 23 - 21 Argentina (Saturday, September 21)
POOL B: New Zealand 23 - 13 - South Africa (Saturday, September 21)
POOL C: Australia 39 - 21 - Fiji (Saturday, September 21)
POOL B: Italy 47 - 22 Namibia (Sunday, September 22)
Pool A: Ireland 27 - 3 Scotland (Sunday, September 22)
Pool C: Enaldn 35 - 3 Tonga (Sunday, September 22)