The Tri Nations champions had endured a frustrating opening half as they struggled for fluency against an aggressive Italian rush defence and the regular whistling of referee Alain Rolland.
Two penalties apiece from Quade Cooper and Mirco Bergamasco made it 6-6 at the interval.
But a devastating burst of four tries in 17 second-half minutes turned the game on its head as Ben Alexander, Adam Ashley-Cooper, James O'Connor and Digby Ioane all went over, with O'Connor adding three conversions.
The Azzurri had looked to close down the playmaking threat of Cooper early on, but paid the price as captain Sergio Parisse was caught offside after getting out of the traps too quickly, but the fly-half pushed his straightforward penalty attempt.
Cooper was then called into action at the other end, sweeping in behind to mop up a Luciano Orquera grubber with Andrea Masi bearing down.
Bergamasco was short with a penalty shot for Italy and a late hit by hooker Leonardo Ghiraldini on Cooper allowed the Wallaby number 10 to register the first points with a 19th minute three-pointer.
They extended their lead as Cooper knocked over his second penalty from close range, but their frustration soon increased as Bergamasco knocked over two penalties late in the half to level the scores and give Italy hope of causing a major upset.
It took just six minutes of the second stanza for Deans to decide changes were needed, with O'Connor replacing Anthony Faingaa.
And the Wallabies soon regained the lead.
Ioane's break and fine link work by Radike Samo gave them the position for prop Alexander to trundle over for a 49th-minute try that made it 11-6, with O'Connor failing to add the conversion.
A second try quickly followed as a stretched Italy defence was cut apart by Adam Ashley-Cooper's angle of support off Cooper. The winger dotted down behind the posts to make the conversion a formality for O'Connor.
Italy were suddenly being ripped open at will and O'Connor was next to cross the line as an inside pass from Cooper allowed the replacement to wriggle past Carlo Antonio Del Fava for a third try, which he converted.
And a bonus point was secured as replacement Luke Burgess and Cooper combined to send Ioane racing over for another converted score.
Italy were denied a deserved consolation late on as Parisse just failed to keep control of the ball after the Azzurri scrum had marched their Wallaby counterparts back over their own line.
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