Cuthbert will reunited with his British and Irish Lions back three partners George North and Leigh Halfpenny as Wales hope the Lions influence can end their own dismal run against the Wallabies.
Wales have won only two of the last 23 meetings and lost to the Wallabies four times in 2012 alone.
Cuthbert, who scored a try in the Lions' first test win in June and has nine from his 18 Wales appearances, has recovered from an injury picked up in a Heineken Cup match a month ago.
The match falls outside the international window but North has been released by his English club Northampton - who are likely to be fined for doing so by Premiership rugby as that breaches the clubs' own code of conduct agreement.
Dan Biggar and Mike Phillips are reunited at halfback after missing Friday's laboured 17-7 win over Tonga while Scott Williams is also back from injury at centre, alongside Owen Williams, who scored a try against Tonga.
"It's great to have Alex and Scott available and they bring a lot of experience into the backline," coach Warren Gatland said in a statement.
"Alex and the medical teams have worked really hard to ensure he is ready for this weekend and it's great to be able to bring him back into the side.
"We are looking to finish the series off well, the last three games against Australia have gone right down to the wire and I don't expect anything different this weekend."
Wales twice lost by two points and once by a single point last year but will need a vast improvement on last week's performance if they are to avoid an 18th successive defeat against the southern hemisphere's big three.
15-Leigh Halfpenny (Cardiff Blues), 14-Alex Cuthbert (Cardiff Blues), 13-Owen Williams (Cardiff Blues), 12-Scott Williams (Scarlets), 11-George North (Northampton Saints), 10-Dan Biggar (Ospreys), 9-Mike Phillips (Unattached); 8-Toby Faletau (Newport Gwent Dragons), 7-Sam Warburton (Cardiff Blues, captain), 6-Dan Lydiate (Racing Metro), 5-Ian Evans (Ospreys), 4-Alun Wyn Jones (Ospreys), 3-Rhodri Jones (Scarlets), 2-Richard Hibbard (Ospreys), 1-Gethin Jenkins (Cardiff Blues).
Replacements: 16-Ken Owens (Scarlets), 17-Ryan Bevington (Ospreys), 18-Samson Lee (Scarlets), 19-Ryan Jones (Ospreys), 20-Justin Tipuric (Ospreys), 21-Rhodri Williams (Scarlets), 22-Rhys Priestland (Scarlets), 23-Liam Williams (Scarlets).
- Sports & Recreation
- George North
- Leigh Halfpenny
- British and Irish Lions