Israel Folau's ankle injury has prompted Cheika to shift Dane Haylett-Petty from wing to fullback and introduce winger Jack Maddocks for his first Test start.
There are four changes in total from the team that lost 38-13 in Sydney last week.
Two of those come at prop in response to a back-pedalling scrum.
Scott Sio returns from injury to replace Tom Robertson on the loosehead side while, in a minor surprise, Brumbies prop Allan Alaalatoa is at tighthead in place of the experienced Sekope Kepu.