Jantjies, who scored a brace on his debut against Australia a week earlier, crossed at the death after coming on as a replacement with South Africa trailing the All Blacks 16-9.
The scrum-half’s dramatic intervention was converted by Handre Pollard to tie the game, ensuring the Springboks continue to lead the way with one round left to play.
South Africa, who will welcome The British & Irish Lions in 2021, took the early lead at the Westpac Stadium in Wellington after fly-half Pollard kicked two early penalties.
But New Zealand forged ahead on the cusp of half-time when Jack Goodhue crossed for the hosts’ only try after a scintillating break from Beauden Barrett, who converted the score.
Barrett and Pollard traded further penalties after the restart before All Blacks fly-half Richie Mo’unga took over kicking duties and added two more penalties.
However, with just one minute left on the clock, the Springboks found Cheslin Kolbe on the right and he chipped forward for Jantjies to touch down.
The television match official was consulted for a potential knock-on as Jantjies challenged for the ball with Aaron Smith, but no infringement was found and the score stood.
That presented Pollard with a chance to level the scores from out wide and he duly obliged to keep South Africa ahead of New Zealand in the overall Rugby Championship standings.
The other round two game saw Australia beat Argentina 16-10 in Brisbane thanks to 11 points from the boot of Christian Lealiifano and a try from Reece Hodge.
With this year’s competition shortened to three rounds due to the World Cup, South Africa can win the Rugby Championship for the first time if they beat Argentina in Salta in their last game.