New Zealand are now one win away from becoming the first team in rugby union history to make a successful world title defence, but they were given a ferocious examination by South Africa's hard-nosed forwards.
Fly-half Dan Carter kicked a drop-goal, two conversions and a penalty, while his opposite number - 21-year-old Handre Pollard - landed five penalties and his replacement Patrick Lambie booted a penalty 11 minutes from time.
But South Africa, who began their World Cup with a shock defeat against Japan five weeks ago, could not quite do enough during a game of unremitting nervous tension, and New Zealand posted a record 13th successive World Cup win.
It was a match of limited try-scoring opportunities, yet the astonishing collision-force of two mighty packs kept an 80,000 crowd gripped for the entirety of a match that underlined why southern-hemisphere rugby is currently some way ahead of any northern nation.
New Zealand made a nervous start as Springboks full-back Willie le Roux sent centre Jesse Kriel charging through following a defence-splitting pass, and, while the All Blacks cleared immediate danger, Carter's clearance kick went straight into touch before Pollard landed a third-minute penalty.
But it only took New Zealand six minutes to settle, and they went ahead when Kaino powered his way to the line for a try in the corner that Carter converted at the second attempt after Springboks wing Bryan Habana was sent back for encroachment following an attempted charge-down.
South Africa, though, gave as good as they got during the opening exchanges, taking the game to New Zealand as Pollard's second successful penalty made it 7-6.
And there was more to come from the Springboks, with Habana taking a brilliant attacking catch that set up an opportunity for Le Roux, whose kick ahead narrowly evaded the clutches of wing JP Pietersen.
But New Zealand were punished for drifting offside in midfield, and Pollard completed his penalty hat-trick midway through a pulsating half.
South Africa were then unlucky not to extend their lead when Pietersen intercepted a Ma'a Nonu pass and was away, only for referee Jerome Garces to take play back and award New Zealand a penalty.
Before Carter could line up his kick, though, Garces consulted assistant official John Lacey and the penalty was reversed for a neck-roll tackle by All Blacks prop Joe Moody on South Africa number eight Duane Vermeulen.
Kaino then blotted his copybook by kicking the ball away from an offside position, which resulted in Garces giving him a yellow card and Pollard booting another penalty for a 12-7 interval lead.
South Africa knew they needed to make their temporary one-man advantage count immediately after the restart, yet it was New Zealand that struck first through Carter's drop-goal.
All Blacks wing Nehe Milner-Skudder then escaped being penalised for obstruction on Habana, but it proved to be his last act of the contest as All Blacks boss Steve Hansen made a first substitution, sending on Barrett.
And Barrett needed hardly any time to make an impact, sprinting over wide out after he collected Nonu's pass for a try that Carter improved from the touchline after Habana received a yellow card for an attempted deliberate knock-on.
The Springboks were now up against it, trailing by five points, before Pollard and Carter exchanged further penalties and New Zealand entered the final quarter of an enthralling contest 20-15 ahead.
Pollard lined up another penalty attempt as South Africa pressed, but it was reversed by Garces for a neck-roll tackle by veteran Springboks substitute Victor Matfield, and New Zealand cleared the danger.
Pollard was replaced by Lambie as Springboks head coach Heyneke Meyer made full use of his bench, and Lambie stepped up to nervelessly land a penalty with 11 minutes remaining.
It proved to be a frantic finale wholly in fitting with a titanic encounter, yet, as the rain fell from leaden skies, New Zealand had just enough in their armoury to turn the lights out on South Africa's World Cup campaign.
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