Italy (14) 20
Pens: Marcato (2), Orquera (2) Drop-goals: Marcato
Australia (14) 30
Tries: Turner, Cooper
Pens: Giteau (5), Mortlock
Cooper (right) scored with seven minutes left against Italy
Italy came close to recording a famous win over Australia but were denied when fly-half Quade Cooper came off the bench to score with seven minutes left.
The debutant touched down with the scores tied at 20-20 after Luciano Orquera missed a 67th-minute penalty.
Lachie Turner's score established an 8-3 lead for Australia but a drop goal and Mirco Bergamasco's try put the hosts in the driving seat at 14-11.
Matt Giteau then hit three penalties but Orquera could only manage two.
The Italian substitute fly-half levelled the scores at 20-20 with two penalties on 53 and 60 minutes, but missed the crucial kick with 13 minutes left, allowing Cooper to take full advantage with a mazy run and score.
Italy coach Nick Mallett was happy with his team's efforts but complained that his captain Sergio Parisse had been blocked on the decisive try.
"I'm very proud with the way we defended against this team and to score a try on first phase, I'm very proud of them," said the former South Africa coach.
"At 20-20 we were right back in the game but I'm very disappointed in the second try.
"There was blocking on Sergio, he's knocked over off the ball and it should never have been awarded.
"That was very disappointing in a game like this, you don't want to lose it like that."
Cooper, meanwhile, was elated to score on his debut.
"I got a great ball from Giteau, space opened up, I saw the line, adrenalin ran through me and I just ran as hard as possible," said Cooper.
"There's too many words to explain how I feel, it's amazing. There's millions of people back in Australia who would love this opportunity, I got it and I took it with both hands."
The result allowed the Aussies to bounce back from the defeat to New Zealand last week and sets them up for their match against England next Saturday at Twickenham.
Italy: Masi, Robertson, Canale, Garcia, M. Bergamasco, Marcato, Canavosio, Perugini, Ghiraldini, Nieto, Del Fava, Bortolami, Sole, M. Bergamasco, Parisse.
Australia: Ashley-Cooper, Turner, Mortlock, Tahu, Ioane, Barnes, Burgess, Alexander, Moore, Dunning, Chisholm, McMeniman, Mumm, Waugh, Brown.
Referee: Bryce Lawrence (New Zealand).