Tries by Jerome Kaino and Beauden Barrett early in each half were a fair representation of the All Blacks’ superior commitment to attack and they deservedly advanced to face Argentina or Australia in the final back at Twickenham next Saturday.
"We did it the hard way today. It was always going to be that way but we've got a crack at it next week," said New Zealand captain Richie McCaw, who now has the chance to become the first man to hoist the Webb Ellis Cup twice.
"We've been saying they would bring everything. There were no surprises and we had to dig deep to get the result."
South Africa led 12-7 at halftime through the goal-kicking of Handre Pollard but spent most of the half defending.
Though they offered precious little in attack all match and kicked badly out of hand the Springboks somehow clawed their way back to within two points with more penalties to set up a nail-biting last 10 minutes.
New Zealand, however, showed all their vast experience to run down the clock and give themselves the chance to become the first country to retain the title.
"We believed we were good enough to beat them but we just weren't," said South Africa coach Heyneke Meyer. "We wanted to make our country proud and we didn't"
Magnificent defence
The majority of the first half was played in the South African half but the Springboks emerged from it five points ahead thanks to magnificent defence and the deadly boot of Pollard.
New Zealand got the only try of the half after seven minutes when McCaw sent Kaino over in the corner and though Dan Carter converted, he struck the post with a later penalty.
There were no such problems for Pollard, whose beautifully struck kicks bisected the posts four times after the All Blacks were continually penalised.
The consolation for the holders was that they would have confidence their rivals would eventually tire and if there was no improvement in their tactical kicking, they would not be able to keep out the relentless black waves.
In fact the South African kicking got worse, inviting attack after attack, and as they lost three successive lineouts, the pressure ramped up, despite the All Blacks playing the first nine minutes of the second half with 14 after Kaino was sin-binned.
Carter slotted a drop goal then the black wave went right and left to create space and send replacement wing Barrett over for a converted try and a 17-12 lead.
A penalty apiece made it 20-15 going into the final 20 minutes and Pat Lambie, on for the injured Pollard, landed a difficult 40-metre kick to reduce the lead to two points.
As the rain lashed down and handling became difficult the two giants of the sport smashed away at each other desperate to find a gap, or force a penalty.
However, after losing their opening game to Japan, South Africa have been playing knockout rugby for five weeks and it appeared to catch up with them.
They briefly threatened when a rolling maul took them into penalty range but New Zealand, lessons learned, made sure they stayed on the right side of the ref.
The holders then took control and, appropriately, ended the game deep in the South African half as they chalked up their 11th, and most important, victory in their last 13 meetings with their greatest rivals.
A record 13 successive wins
How the All Blacks have fared in past RWC finals after their 20-18 defeat of the Springboks gives them a chance to repeat their 2011 heroics.
PLAYING FOR THE CUP - ALL BLACKS' RWC FINAL HISTORY
1987 - v France, Eden Park, Auckland
Hosting the inaugural Rugby World Cup, New Zealand win on home soil after tries to Michael Jones, David Kirk and John Kirwan see them past France. NZ 29-9.
1995 - v South Africa, Ellis Park, Johannesburg
A Joel Stransky drop goal in extra time hands the Springboks an emotional win over their great rivals. Controversy surrounds the tryless match, but the sight of Nelson Mandela, wearing a South Africa jersey, handing the trophy to skipper Francois Pienaar is one of the defining moments of the tournament's history. SA 15-12.
2011 - v France, Eden Park, Auckland
The All Blacks end 24 years of hurt with a nerve-wracking win over a committed French side led by the inspirational Thierry Dusautoir who very nearly upset the party. Fourth-choice first five-eighth Stephen Donald, called into the squad after a host of injuries, kicks a famous penalty while skipper Richie McCaw later reveals he played the final matches of the tournament with a broken foot. NZ 8-7.
2015 - v ?, Twickenham, London
The All Blacks seek to become the first side to win back-to-back World Cups and win a third world title against either Australia or Argentina.
