Rennie lost forwards Anton Segner and Asafo Aumua as well as winger Leroy Carter to injuries and concussions sustained in last week's 50-19 victory, which secured the Bledisloe Cup for a 24th consecutive year.
Josh Moorby has been promoted from the bench to replace Carter on the left wing but most of the injury-enforced changes are to the bench.
Hooker Samisoni Taukei'aho, prop Xavier Numia, loose forward Du'Plessis Kirifi, scrumhalf Cortez Ratima and centre Timoci Tavatavanawai come into the replacements.
Richie Mo'unga is once again unavailable because of a calf injury so Damian McKenzie gets another run in the number 10 shirt after a fine game at Eden Park last week. Beauden Barrett again starts at fullback.
Forward Ethan Blackadder is also unavailable due to injury.
"The Wallabies are a proud side and they'll be hurting after last week," Rennie said in a statement.
"It's a great challenge for us to now face them in front of their home crowd in Sydney."
New Zealand have beaten Australia in their last 12 meetings.
New Zealand Bledisloe II side:
Starters: 15-Beauden Barrett, 14-Will Jordan, 13-Quinn Tupaea, 12-Jordie Barrett, 11-Josh Moorby, 10-Damian McKenzie, 9-Cam Roigard, 8-Wallace Sititi, 7-Peter Lakai, 6-Tupou Vaa'i, 5-Fabian Holland, 4-Scott Barrett, 3-Fletcher Newell, 2-Codie Taylor (captain), 1-George Bower
Replacements: 16-Samisoni Taukei'aho, 17-Xavier Numia, 18-Pasilio Tosi, 19-Shannon Frizell, 20-Du'Plessis Kirifi, 21-Cortez Ratima, 22-Timoci Tavatavanawai, 23-Rieko Ioane
Australia Bledisloe II side:
Starters: 15-Tom Wright; 14-Max Jorgensen, 13-Joseph-Aukuso Suaalii, 12-Isaac Henry, 11-Harry Potter; 10-Declan Meredith, 9-Ryan Lonergan; 8-Harry Wilson (capt), 7-Fraser McReight, 6-Rob Valetini; 5-Jeremy Williams, 4-Lukhan Salakaia-Loto; 3-Allan Alaalatoa, 2-Josh Nasser, 1-Aidan Ross
Replacements: 16-Billy Pollard, 17-Angus Bell, 18-Massimo De Lutiis, 19-Josh Canham, 20-Carlo Tizzano, 21-Kalani Thomas, 22-Harry McLaughlin-Phillips, 23-Filipo Daugunu