New Zealand raced into a 12-5 lead with some scintillating rugby, but once the Springboks settled into their power game they dominated the contest and pulled away on the scoreboard.
The final Test will be played in Baltimore, United States, next Saturday, but there is a morale victory for the Springboks, who won the South African leg of the series and cemented their place as the number one team in the world.
The game started at a breathless pace that was sustained through the first half-hour.
New Zealand scored two tries in that period as number eight Ardie Savea crossed twice before he was forced from the field with an injured shoulder.
His first came from an early period of pressure as he crossed from close range, before wing Kurt-Lee Arendse went over in the corner for the home side as they found some rare space out wide.
Savea picked up from a ruck 10 yards out and also crossed out wide to extend New Zealand’s lead to 12-5, but went off soon afterwards, perhaps a turning point in the game.
“It was a great game from the All Blacks, they pushed us all the way,” Springboks captain Siya Kolisi said. “Those first 25 minutes the lungs were pumping hard, but we did well to make sure we did not concede more points.
“The way we finished this test was better than we have in the previous two.”
The Springboks had lost full-back Cheslin Kolbe to a concussion early on, in a blow to their goal-kicking prowess as well, with Manie Libbok coming on at flyhalf and Sacha Feinberg-Mngomezulu moving to the number 15 position.
Feinberg-Mngomezulu had also been sent to the sin-bin for a deliberate knockdown early in the piece in a chaotic opening.
All Blacks number 10 Ruben Love received a yellow card four minutes from the end of the half for cynical play as he slowed the ball down and prevented a possible Springbok try.
South Africa opted for a scrum from a penalty five yards out and demolished the All Blacks pack, with a penalty try awarded by referee Nika Amashukeli to leave the score at 12-12 at halftime.
“We started really well and created some good momentum in the first half. But the Springboks came out in that second half and played their game. We probably allowed them to do that, and they got on top of us,” All Blacks loose-forward Luke Jacobson said.
“It has been awesome to play over here, it is a country that loves rugby and we have loved playing here. The footie itself is a match-up between the best in the world. It has been awesome to be part of it.
The opening 10 minutes of the second half were cagey, but every time the Springboks secured a scrum, it turned into a penalty as they used the set-piece to get out of territorial trouble a few times.
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New Zealand were the first to score points in the second half when wing Will Jordan’s kick through was collected by fellow wide man Leroy Carter and returned to Jordan to score his 54th international try.
South Africa hit back straight away after soft defence from Carter allowed centre Jesse Kriel to canter in and Feinberg-Mngomezulu’s conversion put the home side ahead 19-17.
The Springboks’ power was on full display when they won yet another scrum penalty, kicked for touch and hooker Malcolm Marx powered over from a 20-yard driving maul. Feinberg-Mngomezulu converted.
A Feinberg-Mngomezulu penalty extended the home lead to 12 points and despite a late try after the hooter for Samisoni Taukei'aho, the home side were able to hold on for the win.