Moore will start as the first-choice hooker in place of Tatafu Polota-Nau in a shake-up following last week's much-criticised 24-19 loss to Scotland in Sydney.
Cheika made three other changes in the forward pack, with ACT Brumbies pair, prop Scott Sio and lock Rory Arnold, joined by Lopeti Timani at No.8 in place of rookie prop Tom Robertson, lock Sam Carter and No.8 Scott Higginbotham.
"Moore's obviously the captain of the team and he's got a lot of experience," Cheika said.
"Polota-Nau's still putting out a big challenge to him and I want to give Moore the chance to respond.
"It's Moore's chance to get back in the starting boots and Polota-Nau's opportunity to finish from the bench, if he gets selected as a finisher."
Moore will become the 10th most-capped international player, surpassing Italian Martin Castrogiovanni and England's Jason Leonard in his 120th Test.
The hooker is 19 games away from Australia's Test record held by George Gregan with 139.
"It's a big week, no doubt, particularly after last week against Scotland," Moore said. "The game can't come quick enough for everyone."
Melbourne Rebels flyer Sefa Naivalu will add to his six Tests, while Rob Horne returns for Tevita Kuridrani to partner Karmichael Hunt in the centres.
- 'Earn that jersey' -
Horne's last Australia appearance was 12 months ago in the final Test against England in Sydney.
Horne will move to English side Northampton next year, putting him out of contention for the 2019 World Cup, and was not in Cheika's original squad until a late injury to Samu Kerevi (ankle).
"We're missing Samu at the moment and there's some other players who I think have been going well in Super Rugby," Cheika said.
"But I think you've got to earn that jersey and Rob Horne, since I've seen him in camp, I think he has."
The Wallabies are taking no risks with winger Henry Speight's hamstring strain that kept him out of the Scotland game.
"We made a decision on Henry early in the week, he still had a bit of pain, there was some risk for him," Cheika said.
"I think considering our position with the competition in the wing spot, that wasn't worth risking for Henry this week and we want to make sure that he's right for the rest of the season as well."
The Wallabies are yet to lose to Italy in their 16 encounters, winning 23-20 in their last clash in Brisbane in 1994.
The Italy Test is the Wallabies' last before August's Bledisloe Cup against New Zealand, with players heading back to their Super Rugby clubs next week for the final two home and away rounds of the competition.