The Wallabies led 28-13 early in the second half at Lang Park, but Italy roared back with 14 uninterrupted points to trail by a point with three minutes remaining.
Flyhalf Bernard Foley thwarted the comeback with a jinking run and try in the 77th minute before replacement back Reece Hodge made the result certain with a brilliant dash down the left touch-line to cross at the final hooter.
Australia rebounded from their surprise 24-19 loss to Scotland last week but the laboured win over 15th-ranked Italy will do little for their confidence ahead of bigger tests against world champions New Zealand in the Rugby Championship.
"It probably shows where we're at a little bit, probably down on confidence a little bit in that game," said Wallabies captain Stephen Moore, reinstated as starting hooker after being relegated to the bench against Fiji and Scotland.
"It probably showed in our attack ... We've got a big, big couple of months ahead to work on before we play New Zealand."
Israel Folau scored two tries in the first half, adding to his doubles against Fiji and Scotland, and became the first Wallaby to score multiple tries in three successive matches.
It was one of the only positives for Michael Cheika's side, who were cruising at 28-13 in the 45th minute before suffering an apparent loss of confidence as their scrum disintegrated in front of a modest crowd of 22,000.
A string of abysmal handling errors set the slide in motion, with scrumhalf Will Genia sending a long pass sailing over Foley's head as the flyhalf streamed down the left flank, unmarked and gunning for the try-line in the 56th minute.
Winger Dane Haylett-Petty then gifted a try to the Azzurri eight minutes later, spilling a high cross-kick by flyhalf Tommaso Allan at the right corner to allow fullback Edoardo Padovani to scamper over.
Three minutes later, replacement back Tommaso Benvenuti intercepted a poor pass from lock Rory Arnold inside the Wallabies' 22 and burst through the cover defence to score a try.
Allan's conversion put the Italians within a point and worse was to come for the Wallabies as replacement flyhalf Quade Cooper squandered a try chance by fumbling a Genia pass at the base of the left post.
Deep in Italy's 22, and after repeated scrum infringements, the Wallabies' front row buckled again, sending replacement prop Toby Smith to the sin-bin.
Down to 14 men with six minutes left, the Wallabies were reprieved when Braam Steyn was also yellow-carded in the 76th minute for pulling down a maul.
A minute later, Genia shot out a pass from under the posts to the quick-footed Foley who burst through for the relieving try.
The flyhalf, nicknamed the 'Iceman', then had a hand in the final try as the explosive Hodge burned away from the Azzurri to score the final try and save the Wallabies blushes.
Italy, beaten by Scotland and Fiji, lost all three of their June internationals but won admirers for their second half fightback.
"I am very proud of my boys," captain Francesco Minto said.
"Most of all I am proud that we played a very committed game and pushed the Wallabies to their limit."
(Reporting by Ian Ransom in Melbourne; Editing by Amlan Chakraborty)
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