Petaia, 18, will become the youngest Wallabies debutant since James O’Connor a decade ago when he starts on the left wing.
Scrum-half Gordon also gets his chance in Padova, with Cheika making six changes of personnel following the 9-6 defeat to Wales.
Ashley-Cooper will win his first cap for over two years on the right wing, so Israel Folau reverts to full-back.
Matt Toomua comes into the side at 10 with Bernard Foley moving to the centres alongside Samu Kerevi as Kurtley Beale drops to the bench.
Full-back Jayden Hayward replaces Luca Sperandio in the only change to the Italy team following their 28-17 victory over Georgia.
Australia: Israel Folau, Adam Ashley-Cooper, Samu Kerevi, Bernard Foley, Jordan Petaia, Matt Toomua, Jake Gordon; Scott Sio, Folau Fainga’a, Taniela Tupou, Izack Rodda, Adam Coleman, Jack Dempsey, Michael Hooper (captain), David Pocock.
Italy: Jayden Hayward, Tommaso Benvenuti, Michele Campagnaro, Tommaso Castello, Mattia Bellini, Tommaso Allan, Tito Tebaldi; Andrea Lovotti, Leonardo Ghiraldini (captain), Simone Ferrari, Alessandro Zanni, Dean Budd, Sebastian Negri, Jake Polledri, Braam Steyn.
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