South Africa clinched a record fourth Rugby World Cup title by doing just enough to deny 14-man New Zealand and retain their crown in a helter-skelter final in Paris.

The Springboks seemed to have control when, with Handre Pollard's dead-eyed goalkicking having already given them a 9-3 lead, Sam Cane caught Jesse Kriel high in the 27th minute.

The New Zealand captain was shown a red card on review and another Pollard penalty left the All Blacks a man down, nine points behind and in deep trouble.

But New Zealand rallied, rode their luck and dragged themselves back into the game. Richie Mo'unga kicked a penalty before the break and Beauden Barrett scooped up a loose ball and slid in after the interval to cut South Africa's lead to 12-11.

Both teams pushed for a decisive score in an enthralling, lactic-drenched final quarter, but neither found one, with Jordie Barrett missing a long-range 73rd-minute penalty and the Springboks clinging on for a third successive one-point victory in the knockout stages.

Captain Siya Kolisi clutched his head in disbelief as he danced off the bench and towards his team-mates on the final whistle. His side are the first team to win the tournament back-to-back away from home - a statistic Leinster-bound coach Jacques Nienaber underlined in the build-up - and are now the undeniable dominant force in World Cup history.

Their latest victory means the Springboks have won half of the eight tournaments they have taken part in. South Africa were absent from the first two editions because of the sporting exile imposed by the rest of the world in reaction to the country's apartheid government.

In that era, the Springboks were hated by many black South Africans. But under the leadership of Kolisi - the team's first black Test captain - they have won backing from across the spectrum of the Rainbow Nation.

Ian Foster's four-year reign as New Zealand head coach ends within a whisker of the ultimate prize, having come under pressure in the build-up when his team dipped below their usual high historical standards.

Springboks hang tough in nail-biter once again

With the Stade de France still ringing to the sound of a full-throttle haka, the two teams tore into each other from the off.

Eben Etzebeth levelled Mo'unga to cheers and groans before Shannon Frizell's desperate attempt to remove South Africa hooker Bongi Mbonami from a breakdown took both players out of the game - one temporarily, one permanently.

On review, Frizell was let off with a yellow for an ugly-looking neck roll clear-out, while the injured Nbonambi, the Springboks' only specialist hooker, was forced out of the game.

Deon Fourie, a converted flanker, came on to replace Nbonambi and, with the man advantage, his side made hay.

Pollard, whose accuracy off the tee helped secure him a starting role, nailed two penalties during the powerplay.

The physicality never dropped. The breakdown was a bunfight. The line-out was a lottery of limbs. The gainline was cratered with big hits. Jordie Barrett and Damian de Allende charged at each other with wild abandon in midfield.

Pollard and Mo'unga traded penalties as the Springboks kept clear at 9-3 up.

But New Zealand, whose indiscipline cost them dear during a warm-up defeat against the Boks at Twickenham in August, strayed over the line of legality once again.

In the midst of some heavy traffic, Cane flew into a collision with Kriel. It was over-eager rather than malicious, but his shoulder to the side of the South Africa centre's head, with no effort to dip, made a red card the likely outcome on review.

Referee Wayne Barnes delivered the news as Pollard lined up another penalty, following good work from Steven Kitshoff.

Pollard landed his kick to dig New Zealand's hole a little deeper and it seemed, with 34 minutes gone and the All Blacks 12-3 adrift, as though the destiny of the contest and the cup might already be decided.

But the All Blacks raged against the script. Rieko Ioane was scragged just short as they chanced their arm on a penalty advantage before Mo'unga slotted a kick shortly after to take his side down the tunnel 12-6 down and still, in theory, in touch.

Their under-staffed defence, caught between shoring up the scrum and covering the threat of South Africa's pacy wings, was stretched thin though.

Kolisi, bearing down on the line after Beauden Barrett dropped a high ball in his lap, should have put Kriel in for a try inside a minute of the restart. Kurt-Lee Arendse came within inches of a score as he chased a seemingly lost cause.

Springboks skipper Kolisi became the third player to go to the sin-bin - his hit on Savea slipping high - and New Zealand, briefly back level in terms of personnel, crowbarred the game open again.

Aaron Smith had already seen a try chalked off for an earlier knock-on when Jordie Barrett slung an enormous pass wide to Mark Telea.

The wing stepped, darted and dropped the ball as he was tackled just short of the line. Crucially it was judged to have gone backwards and Beauden Barrett gathered up and slid over.

Mo'unga's conversion hung wide to leave South Africa in front, but only by a point at 12-11 with 20 minutes remaining.

New Zealand flung everything they had at the Boks, whose defence strained, but stayed intact.

The All Blacks' clearest chance came when South Africa wing Cheslin Kolbe knocked the ball out of the air as he rushed in to tackle a galloping Anton Lienert-Brown.

Kolbe was shown yellow for a deliberate knock-on and Jordie Barrett called for the tee. But the All Black centre's kick - from a tricky angle just inside the Bok half - fell wide and, try as they might, his side could not make the most of another spell back at 14-men apiece for the remainder of the game.

After similarly narrow victories over France and England, South Africa, with Kolisi's legendary 1995 predecessor Francois Pienaar watching on for the final step, have walked the hardest, narrowest route to the trophy.