Bowler Dale Steyn led the way with a four-wicket haul and a final over which included three dismissals and only four runs.
Chasing 171 for victory, New Zealand entered the last over of the contest on 164 for 5, with Ross Taylor well set on 62 off only 36 balls, while Luke Ronchi had five runs to his name off only two balls.
Steyn, up to that point, had captured 2 for 13 in three overs, but it would take something special to see the Proteas to victory. Steyn delivered.
With his first ball, he had Ronchi caught behind by a diving Quinton de Kock, as the Kiwi wicketkeeper thick edged a full ball behind the wicket.
Nathan McCullum, showing his nerves, tried to go for a big hit off Steyn off the first ball he faced, but failed to make contact.
Steyn cranked up the pace all the way to 148 km/h with his next delivery, pitching the ball short of a length outside off and McCullum missed it as he tried to work it to the leg side.
With only three balls remaining McCullum hit Steyn over extra cover for four, lifting the Black Caps to 168 and leaving them needing only three runs off of the remaining two balls.
With the second last delivery of the game, Steyn bowled a short and wide ball to the batsman, who connected with the bottom of his bat.
The ball looped to extra cover and South African captain Faf du Plessis made the catch to end McCullum’s short stay.
The batsmen had, however, crossed and that brought the dangerous and in-form Taylor onto strike. A boundary would be enough to win the game.
With the pressure amped up to 11, Steyn produced a full delivery, wide of off and all Taylor could do was push it back towards the bowler, who calmly completed the run out before streaking off in celebration.
He was chased down and surrounded by his ecstatic team-mates as the Proteas revelled in an astonishing victory.