Captain Kate Gynther scored three goals and Nicola Zagame chipped in with two for Australia, which is one of the gold medal favourites in the event along with the U.S.
"An Olympic game is always going to be hard, and Italy are a quality opposition, so it was a very tough game and we're just happy to come out on top," Gynther said.
Tania di Mario and Federica Radicchi scored twice for the 2012 European champion Italians.
Both countries are past Olympic champions in women's water polo — Australia won gold in 2000 when the women's game made its Olympic debut, while Italy claimed the title four years later in Athens.
Australia will next face Britain, which lost 7-6 to Russia on a late breakaway goal from Evgeniya Ivanova to spoil the host nation's Olympic women's water polo debut. Australia and Russia are even atop Group B.
The eight-team field is broken down into two groups of four. The results from the preliminary stage determine the team's seeding for the quarterfinals.
In Group A, the U.S. earned a hard-fought win against Hungary behind seven goals from 19-year-old Maggie Steffens in her Olympic debut.
"She's a stud, I mean come on, seven goals?" U.S. captain Brenda Villa said. "She's a youngster, but you could never tell in the water. She plays like she's been playing at this level for a long time."
Villa said the U.S., which won silver and bronze in the even but never gold, will concentrate on improving its defensive performance ahead of Wednesday's game against Spain.
"I think we'll lock it down a bit better going forward. Spain's a great team, they scored 11 goals on China, so we're definitely going to have to focus on our defence," she said.
The Spanish on Monday made the most of their women's Olympic water polo debut, using a balanced attack to beat China 11-6. Anni Espar scored three times, while a trio of players — Pilar Pena Carrasco, Maica Garcia and Jennifer Pareja — each scored twice for Spain.
With some sharp outside shooting, the Spaniards broke open a 4-4 game in the second quarter with five unanswered goals to take control halfway through the third quarter.
Ma Huanhuan led China, which placed second at last year's world championship, with three goals.
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