Petaia plays 13 for the first time in his young Test career in one of a number of changes from the Wallabies for the Rugby World Cup clash.
Aged 19, he is the first player born this century to start a Rugby World Cup knockout game in a huge show of faith from head coach Cheika.
Petaia teams up with Samu Kerevi in the midfield while Will Genia will pair up with Christian Lealiifano as the half-back duo this weekend.
Reece Hodge returns from suspension and starts on the wing alongside Marika Koroibete, with Kurtley Beale named to start at full-back.
In the forward pack, Allan Alaalatoa is one of two changes made, along with captain Michael Hooper's return to the XV after being a late withdrawal against Georgia.
Alaalatoa takes the spot of Sekope Kepu while Tolu Latu and Scott Sio start alongside him in the front-row.
Australia: 15 Kurtley Beale, 14 Reece Hodge, 13 Jordan Petaia, 12 Samu Kerevi, 11 Marika Koroibete, 10 Christian Lealiifano, 9 Will Genia, 8 Isi Naisarani, 7 Michael Hooper (c), 6 David Pocock, 5 Rory Arnold, 4 Izack Rodda, 3 Allan Alaalatoa, 2 Tolu Latu, 1 Scott Sio
Replacements: 16 Jordan Uelese, 17 James Slipper, 18 Taniela Tupou, 19 Adam Coleman, 20 Lukhan Salakaia-Loto, 21 Nic White, 22 Matt To'omua, 23 James O'Connor
Date: Saturday, October 19
Venue: Oita Stadium, Oita
Kick-off: 16:15 local (08:15 BST, 07:15 GMT)
Referee: Jérôme Garcès (France)
Assistant referees: Romain Poite (France), Mathieu Raynal (France)
Television match official: Ben Skeen (New Zealand)