Lock Sam Darry and flanker Peter Lakai were also brought into the pack on Thursday.
The backline was unchanged after losing the second Test 33-26 last Saturday in Cape Town.
Taylor started all five Tests this year, with Aumua his primary back-up, including the first two matches against the Springboks. In the process Taylor took his career tally to 111 Tests.
But Aumua will start the third match on Saturday at FNB Stadium with the four-Test series locked at 1-1, and Samisoni Taukei'aho on the bench.
Darry gets his first involvement in the series with a start at the expense of Fabian Holland, who goes to the reserves.
Lakai came off the bench in both Tests and has the No.6 jersey after Simon Parker was jettisoned from the match 23.
Wallace Sititi is the impact loose forward for his first chance in the series.
Lock Tupou Vaa'i will play his 50th Test match.
"The team that doesn't win this weekend can't win the series," All Blacks coach Dave Rennie said in a statement. "That's the kind of challenge we love to rise to."
South Africa named their team on Monday, replacing injured fullback Damian Willemse with Cheslin Kolbe, and filling the vacant wing with Kurt-Lee Arendse.
New Zealand: Damian McKenzie, Will Jordan, Quinn Tupaea, Jordie Barrett, Leroy Carter, Ruben Love, Cam Roigard; Ardie Savea (captain), Luke Jacobson, Peter Lakai, Sam Darry, Tupou Vaa'i, Tyrel Lomax, Asafo Aumua, George Bower. Reserves: Samisoni Taukei'aho, Xavier Numia, Fletcher Newell, Fabian Holland, Wallace Sititi, Kyle Preston, Anton Lienert-Brown, Josh Moorby
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