Deans' team looked unnerved by the wet conditions and on-rushing men in blue - even though both were forecast - and they didn't score a point until the 19th minute, when Quade Cooper kicked the first of his two penalties.
They were all Australia had to show for their dominance, but they didn't look like cracking the Azzurri defence.
"You've got to give Italy credit as well," Deans said. "They are a very good defensive side and they take some breaking down."
Italy came back to even things up with successive Mirco Bergamasco penalties.
Australia finally clicked 10 minutes after the break when Digby Ioane combined well with Radicke Samo and Kurtley Beale to tie the Azzurri defence in knots.
James O'Connor, a replacement for Anthony Fainga'a, chimed in, before prop Ben Alexander dived over.
The Wallabies were beginning to get some front-foot ball, and firstly Ashley-Cooper and then O'Connor ran through some tired-looking defence for tries.
Ioane deservedly bagged a five-pointer. He was a handful in the second half and always seemed on the verge of a half break.
O'Connor doesn't always get his timing right - he was dropped by Deans after sleeping in and missing the official Australia team naming - but he made the most of his opportunity yesterday after coming on in the 47th minute.
"There's no doubt I want my position back but I want what's best for the team, too," O'Connor said afterwards.
Italy refused to give up despite the torrent of tries. No 8, Sergio Parisse, always sailing close to the offside line, showed some great skills and tenacity.
He went close to a pushover try late in the match, but those outside him rarely posed a threat. The backs stood very deep - a rarity in international rugby these days - and their moves were telegraphed.
For Australia, Ioane was their danger man and Beale was a class act at fullback. Captain James Horwill was reliable in the lineout and Samo improved as the game went on.
Horwill agreed Australia would have to tidy up on their discipline. The Wallabies were taken to task at the breakdown by Rolland, and Dan Vickerman's back chat after one penalty earned a 10m march up the field which put Italy into a kicking position.
"We were a little bit slow to react at times," Horwill said. "Not all the penalties were for the same things, but some were for silly things like backchat."
Italy coach Nick Mallett paid credit to Australia's attacking ability in the second half. "When they get quick front foot ball they are a very difficult team to defend against," he said.
As for the scrum, which almost resulted in a pushover for Italy in the dying minutes, he said: "We went forward so fast Sergio couldn't control it."
That won't make nice reading for Deans or the Wallabies forwards.
