New Zealand sealed victory with a six off the penultimate delivery as they reached the World Cup final for the first time with a four-wicket win.
With five needed from two balls, Grant Elliott hit Dale Steyn into the stands to finish unbeaten on 84 in Auckland.
Elliott and Corey Anderson’s 58 had lifted the Black Caps from 149-4 in their chase of a weather-adjusted 298.
South Africa had earlier posted 281-5, with Faf du Plessis making 82, either side of a near two-hour rain delay.
Captain AB de Villiers weighed in with an unbeaten 65 for South Africa and David Miller an 18-ball 49 in a target that was escalated by Duckworth-Lewis, but just within New Zealand’s reach.
It was a fourth unsuccessful World Cup semi-final for the Proteas to add to two defeats and the famous 1999 tie with Australia.
For New Zealand, a seventh last-four tie finally yielded a place in the final after six previous losses.
It was earned in a thrilling, fluctuating contest played out in front of a raucous and partisan crowd at Eden Park.
In scarcely believable drama that had echoes of Kane Williamson’s six to defeat Australia by one-wicket earlier in the tournament, South Africa-born Elliott smashed Steyn for six over long-on two balls after Daniel Vettori guided the ball to the third-man boundary.
Elliott should have been caught from the final ball of the previous over, but his top-edged hook fell to the ground after a boundary collision by JP Duminy and sub fielder Farhaan Behardien.
That South Africa came so close was down to their third comeback of a game that both teams controlled at various points.
The Black Caps were in the early ascendancy thanks to some dangerous swing bowling and electric fielding that reduced South Africa to 114-3 in the 27th over.
Twitter reaction
Kevin Pietersen: “South Africa DID NOT CHOKE. They got beaten by a better team today. AB led the team wonderfully well. But, well done NZ. See you in Sydney.”
Australia head coach Darren Lehmann: Congrats @NZcricket1 and congrats @BrendanMcCullum and team, loved the ANZAC spirit, well done to Grant Elliott!
Shane Warne: “Please hold your heads high South Africa, you’ve done everyone proud as you gave it absolutely everything. Congratulations to the NZ team who were outstanding in their run chase.”
Later, they looked to be sprinting through the run-chase when captain Brendon McCullum destroyed the South Africa attack with a 22-ball half-century that included taking 24 runs from a single Steyn over.
South Africa, though, resisted, just as they had earlier through Du Plessis’ patience, De Villiers’ invention and Miller’s explosive power.
Their defiance in the field came with some help from the home side, as McCullum slapped Morne Morkel to mid-on, Williamson pulled the same bowler on to his own stumps and Martin Guptill was run out in a mix-up with Ross Taylor.
And, when Taylor was caught down the leg side from the off-spin of Duminy, New Zealand still needed 139 from 22 overs.
They were pulled back into contention thanks to the watchful Elliott, who was strong through the covers, and the force of Anderson in a partnership of 103.
De Villiers missed the chance to run out Anderson on 33, failing to gather the ball at the non-striker’s end with the left-hander well short of his ground.
The reprieve was the start of New Zealand’s acceleration towards their target, but after Anderson skied Morkel to square leg with 46 still needed, South Africa clawed their way back once more.
The requirement got down to 23 from the final 12 balls, with 11 runs taken from a Morkel over that included the Elliott reprieve.
A tie would have taken the Black Caps to the final because of their superior group record, but Elliott ensured the co-hosts won outright.
