Brisbane - Australia scored two late tries as they survived a fightback from Italy to win 40-27 on Saturday and avoid a second straight defeat.
The Wallabies were 21-13 ahead at half-time and then increased their lead to 28-13, before Italy scored two converted tries to get within a point at 28-27.
But Bernard Foley and Reece Hodge both crossed in the final minutes to stave off the threat of a second loss after last week's shock reverse to Scotland.
The win will do little to ease the pressure on the hosts, who were criticised ruthlessly both by media and supporters following the 24-19 loss to Scotland.
Italy, the Six Nations wooden-spooners, came into the match after consecutive losses to Scotland and Fiji and without a win against Australia in their 16 previous meetings.
The visitors opened the scoring in just the second minute with a Tommaso Allan penalty, before they were denied minutes later when lock Dean Budd appeared to score in the corner.
However, the television match official ruled that winger Giovambattista Venditti's boot had scraped the touchline with one fingertip still touching the ball as he passed infield to Budd.
The Wallabies, who had hardly been in the Italian half, hit the lead after 15 minutes when Sefa Naivalu scorched 40 metres down the touchline to score.
Foley converted to make it 7-0, which became 14-0 minutes later when Israel Folau scored in the corner.
Folau was in again 10 minutes before the break when inside centre Karmichael Hunt found the fullback with a long, flat pass to beat the Italian defence.
However, the Italians struck back just before the break with a superb try to outside centre Michele Campagnaro, who burst onto a ball following a midfield break by Venditti and outpaced the Wallaby defence.
Five minutes after the restart Naivalu crossed for his second following some slick backline work from the Wallabies, including a between-the-legs pass from Foley.
The Italians refused to give in and they got back into the contest when Wallabies winger Dane Haylett-Petty spilled a cross-field kick into the arms of Italian fullback Edoardo Padovani, who scored in the corner.
Australia's lead shrank to 28-27 when replacement Tommaso Benvenuti intercepted a Rory Arnold pass in the Australian 22 and crossed despite Folau's desperate tackle.
The Wallabies lost prop Toby Smith to a yellow card for repeated scrum infringements, but Italy also went down to 14 men when Abraham Steyn was yellow-carded for playing the ball while on the ground.
Foley burst through the Italian defensive line to settle Australian jitters, and then Reece Hodge grabbed a try at the death as he burst down the line.