Jordie Barrett, whose late kick secured the title in a 19-17 victory over the Springboks last week, looked to have sealed a sixth win from six for New Zealand in similar fashion on the Gold Coast on Saturday.
That was until Jantjies struck with the final action of an enthralling contest to end a 10-match winning streak for Ian Foster's men.
Lukhanyo Am's terrific behind-the-back pass led to Damian de Allende's opening try before an exchange of penalties kept South Africa five points ahead.
New Zealand levelled when Sevu Reece just made the corner after a fine Beauden Barrett kick, and despite another Handre Pollard penalty, the All Blacks were soon in command.
A fast, flowing move ended with Ardie Savea going over under the posts and Brad Weber added another try two minutes later following a lineout steal.
Then, momentum shifted. Pollard made no mistake with two more penalties to close the gap to three points, and the Boks were ahead 53 minutes in when Makazole Mapimpi crossed in the corner after the ball was worked from the opposite flank.
Replacement Jantjies stretched the lead further with another penalty, only after play was brought back after an advantage when Faf de Klerk fumbled at the breakdown barely a metre from the try line.
Jordie Barrett reduced the arrears as tensions began to build, although the Hurricanes back kept his cool to kick his side into the lead with five minutes left after South Africa was penalised for holding on.
A gripping finale saw Jantjies sink a brilliant drop goal a minute later only for Jordie Barrett to send another late kick sailing through the posts in what looked like a repeat from a week ago.
But South Africa came again, a lineout inside the New Zealand 22 leading to a penalty right in front of the posts, from which Jantjies made no mistake.