The All Blacks will wrap up the trophy in the Christchurch encounter with two games to spare if they beat the Springboks with a bonus point and if Australia beat Argentina in the other fourth-round match in Perth.
The 22-year-old Savea replaces Sam Cane, who will miss the remainder of the championship after suffering a serious hamstring injury against Argentina last weekend.
Matt Todd has been named as the replacement loose forward cover, while Lima Sopoaga has been added to the reserves for Aaron Cruden, who has been sidelined by a groin strain.
The powerful Savea, a brother of All Blacks wing Julian Savea, has been on New Zealand's radar since being named as an "apprentice" to accompany the side on their northern tour four years ago, although he never played a game.
He did not break into the side until this year when Richie McCaw's retirement opened up a berth behind Cane, leaving Savea to play the first five Tests of 2016 off the bench.
The All Blacks have been the dominant side in the Rugby Championship this year, winning all three games with a bonus point.
Last week, they thrashed the Pumas 57-22 while South Africa, with only one win to date, are coming off a 23-17 loss to Australia last week.
However, All Blacks coach Steve Hansen found several flaws in their win over Argentina, despite the convincing margin - the lineout and defence around the ruck in particular - which the South Africans would also have noted.
"We know they'll be hurting and desperate to get a result after their loss on the weekend. Therefore, our personal preparation this week will have to be at the highest level - bone deep with real clarity," Hansen said.
"We've worked hard this week on improving in the areas we felt weren't good enough last weekend. We're confident that those areas have been addressed and our performance will be improved.
"Whilst we have been reasonably happy with our three games to date ... we are always striving for improvement and with South Africa having their backs to the wall, we know nothing but our best will be good enough. Accuracy with intensity will be paramount."
15 Ben Smith 14 Israel Dagg, 13 Malakai Fekitoa, 12 Ryan Crotty, 11 Julian Savea, 10 Beauden Barrett, 9 Aaron Smith, 8 Kieran Read (captain), 7 Ardie Savea, 6 Jerome Kaino, 5 Samuel Whitelock, 4 Brodie Retallick, 3 Owen Franks, 2 Dane Coles, 1 Joe Moody
Substitutes: 16 James Parsons, 17 Wyatt Crockett, 18 Charlie Faumuina, 19 Luke Romano, 20 Matt Todd, 21 TJ Perenara, 22 Lima Sopoaga, 23 Anton Lienert-Brown
15 Johan Goosen, 14 Bryan Habana, 13 Jesse Kriel, 12 Juan de Jongh, 11 Francois Hougaard, 10 Elton Jantjies, 9 Faf de Klerk, 8 Warren Whiteley, 7 Oupa Mohoje, 6 Francois Louw, 5 Pieter-Steph du Toit, 4 Eben Etzebeth, 3 Vincent Koch, 2 Adriaan Strauss (captain), 1 Tendai Mtawarira
Substitutes: 16 Malcolm Marx, 17 Steven Kitshoff, 18 Lourens Adriaanse, 19 Franco Mostert, 20 Willem Alberts, 21 Jaco Kriel, 22 Morne Steyn, 23 Damian de Allende