You are not permitted to download, save or email this image. Visit image gallery to purchase the image.
The Wallabies showed enough scrambling defence to keep the Italians at bay in perfect conditions in the rugby-mad Italian town of Padua, but dropped balls, mix-ups in attack and scrum penalties marred the win, only their fourth in their last 12 tests.
Australia scored four tries to one to register their first win on their European tour. Winger Marika Koroibete ran in two and prop Taniela Tupou and replacement scrumhalf Will Genia one apiece, but several opportunities went begging.
With England awaiting them next weekend at Twickenham, and the World Cup beckoning in less than 12 months, the Wallabies have still to settle on their best flyhalf and inside centre combination and make their back three fully click on attack.
"I feel great. We won, we grinded. In the change rooms people were smiling," captain Michael Hooper said. "It was a win and we have not had a huge amount (of them) this year."
Cheika, who began his coaching career in Padua, said he was happy with the performance, praising his team's defence which kept Italy at bay while prop Scott Sio, yellow-carded for a deliberate knock-down, was off the field.
He also lauded Matt To'omua's performance at flyhalf in place of Bernard Foley, who was shifted to inside centre after Australia's narrow loss to Wales last weekend.
However, the Wallabies leave for Twickenham with a doubt over the fitness of number eight David Pocock, who can turn games with his steals at the breakdown. He was floored by a collision in the second half and left the field nursing his neck. "We'll see how he recovers," Cheika said.
Italian winger Mattia Bellini scored the home side's try, scooping up a wayward pass from Foley soon after the break, but Italy's coach Conor O'Shea voiced outrage that they had been denied a try in the opening minutes.
Scrumhalf Tito Tebaldi intercepted a pass and bolted under the posts but was judged to be offside without a video review.
"I'm angry," O'Shea said. "For the life of me, why don't you go upstairs when it's there. It's just beyond belief."
Australia and Italy have met 18 times, with the Wallabies winning each time.