The Wallabies quickly opened up a 16-3 lead, including a try from Nick Cummins.
Robert Barbieri was sin binned after 29 minutes, leaving Italy a man short. Australia continued to press in the first half, taking a 22-6 lead into the break.
The home side were quick out of the blocks in the second half, Barbieri scoring a try in the opening minute.
Luciano Orquera added two penalties to bring Italy to within three points with over 20 minutes still to play.
Italy continued to press but Australia's defence appeared to be holding until Digby Ioane was shown a yellow card with two minutes remaining to leave the visitors with only 14 men.
Italy were awarded a penalty with just over a minute left on the clock, but Orquera fired it wide, allowing Australia to hold on for the win.