Level at 6-6 with Italy at halftime, the Wallabies scored three tries in nine minutes through Ben Alexander, Adam Ashley-Cooper and O'Connor to ensure their 16th straight victory over the Azzurri.
Digby Ioane also crossed to earn the Wallabies a bonus point in front of 25,731 fans at North Harbour Stadium for the Pool C match.
Mirco Bergamasco kicked two penalties for an Italian team which rarely threatened the tryline after expending all of its energy in defence. The Italians missed just 3 of 65 tackles in a first half in which the Wallabies had 73 per cent of the territory.
Australia captain James Horwill said the Wallabies had plenty to work on, but took positives from the match.
"It's good start to the campaign. It was an important win for us, to get the bonus point as well," he said.
The Wallabies scrum and lineout held firm in the face of the expected onslaught from the Italian set-piece specialists, buckling once on the Azzurri ball in the first half and being shunted back near fulltime but otherwise providing a solid platform.
"Pleased with the scrum for the most part. Happy with the progress we're making there," Australia coach Robbie Deans said. "Most importantly, getting that result was key. I've got a lot of respect for the Italian side. They're a tough side."
Instead, it was some sloppy handling from the team and an erratic performance from Quade Cooper that cost Australia in the opening 40 minutes.
The flyhalf cleaned up a clever grubber in-goal before Italy fullback Andrea Masi could touch down in the eighth minute. But he also missed a 40-meter penalty from close to in front, and his passing missed its mark on more than one occasion to force the Wallabies backline across field and often into touch.
After Bergamasco missed a shot at goal, Cooper gave Australia the lead with a successful shot in the 18th minute.
Seven minutes later, Ashley-Cooper almost reined in a grubber to score in the corner after a smart interchange of play and some angled running in the Wallabies backs. But one of 15 first-half penalties blown by Irish referee Alain Rolland relieved the pressure on Italy's line.
Australia's scrum allowed the backs to get over the gain line and recycle possession quickly, resulting in another penalty from Cooper in the 30th for a 6-0 lead.
The Wallabies were having trouble linking play on the few times they breached the line, David Pocock being caught isolated on one occasion and Cooper running into a teammate after a counterattacking 50-meter run from a turnover inside his own quarter.
Bergamasco punished Australia for its prolificacy, kicking two penalties in last three minutes of the first half with Cooper again culpable.
Deans saw enough after only eight minutes of the second half to replace Anthony Fainga'a with O'Connor. That move forced the versatile Ashley-Cooper to move in to his preferred spot at outside centre after being targeted by Italy on the wing and dropping several box kicks.
Two minutes later, Australia scored. A stolen lineout ball allowed Ioane to run through a yawning hole up the middle and link with Kurtley Beale and Radike Samo. The ball was recycled, and Alexander crossed over out wide for an unconverted try for an 11-6 Australia lead.
Italy coach Nick Mallett isolated that lineout turnover as the turning point in the match.
"Unfortunately, that 20-minute patch in the second half ... that was very costly," Mallett said. Australia "is a very good side. I'm proud of the way my guys performed.
"I was happy to get through this game without getting humiliated."
The lead jumped out to 25-6 within four minutes. Cooper finding Ashley-Cooper running an outside-in line to cross untouched, and O'Connor then jinking through the middle of tiring Italian team.
Cooper also had a hand in Ioane's 67th-minute try in a much improved display after the break, cleverly turning the ball inside for the powerful winger to straighten the attack and charge over the line.
Nothing went right for Italy in the second half, not even when its scrum-happy pack had an attacking set-piece five meters out. The Wallabies forwards doing just enough to deny the Azzurri a late try.
"It's a pity we didn't control the ball a little bit better," Mallett said. "But give Australia a lot of credit. They managed to win their scrum."
Australia 32 (Ben Alexander, Adam Ashley-Cooper, James O'Connor, Digby Ioane tries; Quade Cooper 2 penalties, O'Connor 3 conversions) def. Italy 6 (Mirco Bergamasco 2 penalties). Halftime: 6-6.