A fourth consecutive trip to the Cricket World Cup semifinals is just a few miles from New Zealand, thanks to an excellent captain's strike and full performance.
Driven inevitably by a magnificent century of Kane Williamson and chilled by the powerful Colin of Grandhomme, the Black Caps remained undefeated after their toughest game to date and finished with South Africa hopes for a third consecutive tournament.
He was tense, though. New Zealand chased 242 with three balls to spare for a four wicket win in Edgbaston, Birmingham, with Williamson 106 not out of 138 balls and Grandhomme 60 out of 47.
De Grandhomme, also a major contributor to the ball, made 14 off off with 12, which left Williamson and Mitchell Santner to finish. A delicate look at the four, then a six jump off Andile Phehlukwayo in the second round of the final did the trick to the captain coolhead.
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The Black Caps remain undefeated and return to the top of the table, with probably only one win in the four remaining games, starting with the West Indies on Sunday (NZT) to reach the top four. South Africa, however, seems to have gone with just one win in six, having lost to New Zealand in the quarter-finals of 2011 and the semi-final epic of 2015.
In a tricky pitch, the Black Caps were always ahead of the chase, but they could not get away.
They had a bit of luck, in a dramatic 38th, the last hurled by the lively Perneiral Imran Tahir (0-33).
De Grandhomme, 22, was eliminated by David Miller with one hand only after Williamson was disqualified in 76 in the final of Tahir's game.
He looked startled to appear to challenge a goalkeeper Quinton de Kock who inexplicably did not appeal. Tahir was more interested, then was in agony when Snicko's replays showed a touch at the end of Williamson's cue.
The way Colin Munro started, the chase seemed a non-contest. He hit Kagiso Rabada through the outside by successive limits in the first, but things changed when South African spearhead changed angle.
Of all the wicket he squeezed Munro, who offered a catch back looping off the inside edge, leaving his point and Henry Nicholls' option an ongoing issue.
Williamson and Martin Guptill fought for the early lead but set up a solid platform before New Zealand lost 3-8 in a 20-ball bizarre and the game was 80-4.
Guptill (35 off 59) pulled, spun and took off for a single regulation just to lose his balance and step on his stumps.
Ross Taylor, second ball, was strangled by the side of the leg by Chris Morris, who almost looked apologetic, so the South African quickly produced a gem to eliminate Tom Latham.
It was all in Williamson, then. If he went through, the black caps were at home.
He walked from one side to the other, unleashed a few straight plays and chose Tahir impeccably, passing 50 years for the 50th time on an international day with 72 balls.
Jimmy Neesham (23, 34) was back in the limelight and helped his captain add a vital 57, but the allrounder stumbled at a crucial moment, knocking Morris out with a big slide.
With 105 accurate of 17.4 overs he demanded some Grandhomme strokes to ease the mounting pressure and he delivered in familar turf where he played for Warwickshire. In the second ball, he scornfully attacked Morris until the middle of the runway. Then, on both sides of Tahir's dramas, he sent Phehlukwayo and Rabada to the stands, New Zealand's nerves at last calmed down and his finisher took over.
Having won the bid after a 90-minute delay for a wet out-field, the Black Caps were in the box position in the innings range, with the championship reduced to 49 overs for each side.
South Africa's 241-6 was below par, but not as much as it looked in a field described as "sticky" by its best scorer, Rassie van der Dussen (67 not out of 64). South Africa has evaluated it as a surface area of 250-260; New Zealand was polished and used the conditions effectively with cruisers and changes of pace.
From Grandhomme (1-33 out of 10) hit the brakes on a surface that fit, Matt Henry (0-34) was accurate and miserable and Lockie Ferguson (3-59) provided some punch at key moments.
His yorkie hunter seized Captain Faf du Plessis' great shutter, and no South African beater actually took over until van der Dussen attacked death.
Ferguson put a tough chance off of Henry in the penultimate place, so his final ended up 15 as van der Dussen was 6, 4 out of the last two deliveries to give the Proteas hope they could make it tricky for New Zealand.