Fly-half Pollard and scrum-half Reinach replace Sacha Feinberg-Mngomezulu, now on the bench, and Grant Williams, who is unavailable due to a "niggle".
The changes were predictable as Feinberg-Mngomezulu, playing only his second match after injury, and Williams performed poorly in a 33-16 first Test loss last Saturday.
A third alteration to the team that fell in Johannesburg is Ethan Hooker coming in on the left wing in place of Kurt-Lee Arendse.
Arendse, who went off concussed early in the match at Ellis Park, moves to the right wing in place of Cheslin Kolbe, another "niggle" casualty.
There could yet be a fourth change to the starting line-up. If flanker Siya Kolisi is passed fit after a hamstring injury he will replace Paul de Villiers.
"Handre has delivered for us under extreme pressure, and we feel that is what he and Cobus have the potential to bring at the beginning of the game," said head coach Rassie Erasmus.
"Then we have Morne (van den Berg) and Sacha coming on later with their different styles of play that will be good for us this weekend.
"Cheslin and Grant suffered niggles last weekend, which ruled them out of contention for selection. We have bracketed Siya alongside Paul to allow us time to monitor how Siya comes through training this week."
The All Blacks are embarking upon their first full tour of South Africa since 1996! Marketed as the 'Greatest Rivalry' series, the winner will come out not only with the bragging rights but World Rugby's number one ranking. Keep up to date throughout August and September with news, previews and more.
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Loose forward Pieter-Steph du Toit will continue as captain and is set to win his 100th cap on Saturday, one week after centre Damian de Allende reached the milestone.
Ox Nche, widely regarded as the best loosehead prop in the world, will make his 50th appearance for the Springboks.
The bench has been reshuffled with only two survivors from the first Test -- 'hybrid' player Andre Esterhuizen, a centre who can play as a loose forward, and prop Gerhard Steenekamp.
Among those promoted is Deon Fourie, who will celebrate his 40th birthday in September. He can operate as a hooker or flanker.
Should he take the field, Fourie will become the oldest Springbok to play in a Test, surpassing Victor Matfield and Schalk Brits, who were 38 years old in their final Tests.
South Africa team to play New Zealand:
Starters: 15-Damian Willemse; 14-Kurt-Lee Arendse, 13-Jesse Kriel, 12-Damian de Allende, 11-Ethan Hooker; 10-Handre Pollard, 9-Cobus Reinach; 8-Jasper Wiese, 7-Pieter-Steph du Toit (capt), 6-Siya Kolisi or Paul de Villiers; 5-Ruan Nortje, 4-Eben Etzebeth; 3-Wilco Louw, 2-Malcolm Marx, 1-Ox Nche
Replacements: 16-Deon Fourie, 17-Gerhard Steenekamp, 18-Thomas du Toit, 19-Lood de Jager, 20-Andre Esterhuizen, 21-Cameron Hanekom, 22-Morne van den Berg, 23-Sacha Feinberg-Mngomezulu
