Australia edged Italy 22-19 in Florence having led 22-6 at the break.
The hosts had a chance to snatch a draw with two minutes to go, but flyhalf Luciano Orquera’s penalty sailed just wide.
The Wallabies looked set for a big victory when they were 22-3 ahead at one stage in the first half after winger Nick Cummins had scored a try in the 18th minute.
But Italy hit back early in the second half with a try to flanker Robert Barbieri, and two penalties from Orquera made it a three-point ball game. However, he failed to kick the ball through the posts in the 78th minute and Australia escaped with the win.