The Springboks beat the Wallabies 35-17 on Saturday despite Rassie Erasmus leaving out a string of key men at Ellis Park.
Director of rugby Erasmus' decision to make changes did not backfire, as scrum-half Herschel Jantjies scored two tries in an impressive debut.
Erasmus flew out to New Zealand soon after the victory along with his coaching staff and eight players - including the likes of Eben Etzebeth, Jesse Kriel, Pieter-Steph du Toit.
Fourteen Springboks had already departed two days before the win over Australia to gear up for a showdown with New Zealand in Wellington on Saturday.
Francois Louw, Marcell Coetzee, Tendai Mtawarira and Schalk Brits are among another 10 who will board the plane on Sunday.
South Africa take on Argentina in Salta on August 10 after doing battle with the world champions.
South Africa squad:
Forwards: Schalk Brits, Marcell Coetzee, Lood de Jager, Thomas du Toit, Pieter-Steph du Toit, Rynhardt Elstadt, Eben Etzebeth, Lizo Gqoboka, Steven Kitshoff, Vincent Koch, Francois Louw, Frans Malherbe, Malcolm Marx, Bongi Mbonambi, Tendai Mtawarira, Franco Mostert, Trevor Nyakane, Marvin Orie, Kwagga Smith, RG Snyman, Duane Vermeulen.
Backs: Lukhanyo Am, Damian de Allende, Faf de Klerk, Andre Esterhuizen, Warrick Gelant, Elton Jantjies, Herschel Jantjies, Cheslin Kolbe, Jesse Kriel, Makazole Mapimpi, Sbu Nkosi, Willie le Roux, Handre Pollard, Cobus Reinach, Frans Steyn.