The Springboks hold an unassailable 2-0 series lead ahead of the match in Port Elizabeth but have been forced to bring in full-back Gio Aplon, inside centre Wynand Olivier, who is promoted from the bench, and Potgieter.
Making way for the trio are full-back Patrick Lambie (ankle) and flanker Willem Alberts (knee), who were both injured in the second Test, while centre Frans Steyn will skip the contest because it clashes with his wedding.
Meyer also made two changes to his replacements with number eight Ryan Kankowski coming in for Keegan Daniel and fly-half Elton Jantjies, who has yet to earn a Test cap, taking Olivier's place on the bench.
Jean de Villiers, who had originally been named South Africa captain for just the England series, has had the appointment extended for the rest of the year.
"Jean has been unbelievable as captain and has matched my expectations," Meyer said.
"We want to plan for the rest of the year. It is always important to have a special leader to gel the team and there is a lot of respect for him from the players.
"It was very easy to make him captain. I have worked with a lot of good captains and he is right up there," Meyer added.
De Villiers said that being appointed captain for the rest of the year would hopefully benefit him and the team.
"It's nice to have that sort of stability. It will give me more time to prepare and work a bit more with management," De Villiers added.
"It's a job that you can't do on your own and the support I have received from the senior players has been unbelievable,"
South Africa have lost two full-backs in as many weeks through injury with Zane Kirchner being ruled out after the first Test but Meyer said that he was excited what the fleet-footed Aplon would bring to the team.
"I've always rated Gio. He brings something different. When we started I wanted a conservative fullback but I picked Gio for his strengths," the coach said of a player capped 16 times by South Africa.
"He can do something magic from the back. He runs great lines, has unbelievable feet and brings an X-factor.
"He has looked good in training and there is no pecking order and if he shows and proves that he is the best full-back, then there is no reason why he can't play going forward."
Meyer said that the uncapped Potgieter was a big ball-carrying blind-side flanker who could give the team momentum on attack but could also stop the opposition.
Team: 15-Gio Aplon, 14-JP Pietersen, 13-Jean de Villiers (captain), 12-Wynand Olivier, 11-Bryan Habana, 10-Morne Steyn, 9-Francois Hougaard, 8-Pierre Spies, 7-Jacques Potgieter, 6-Marcell Coetzee, 5-Juandre Kruger, 4-Eben Etzebeth, 3-Jannie du Plessis, 2-Bismarck du Plessis, 1-Tendai Mtawarira.
Replacements: 16-Adriaan Strauss, 17-Werner Kruger, 18-Flip van der Merwe, 19-Ryan Kankowski, 20-Ruan Pienaar, 21-Elton Jantjies, 22-Bjorn Basson