Stoner, riding a Ducati, started from pole position and held off Yamaha's Rossi to win his home GP for the third straight year. Spain's Dani Pedrosa was third on a Honda, 22.618 seconds behind world championship leader Rossi.
Stoner, who celebrated his 24th birthday on Friday, was making just his second start after a three-race break from the MotoGP circuit caused by a debilitating illness. He finished second on his comeback at the Oct. 4 Portuguese GP.
He said his decision to take a 10 week break to overcome his mystery ailment was now paying off, with his win Sunday moving him into third place on the world standings.
"I think without taking that time off we wouldn't be anywhere near the podium step today, things would have been too difficult for me and physically I wouldn't have been able to last the race," Stoner said.
"It's just been fantastic to come back and get a second in Portugal and almost enough pace to win it, and here have the pace to win. I can't ask for more," he added. "We definitely made the right decision to take that time off and find our way."
After capturing his second straight pole position at the Phillip Island circuit, Stoner was able to dominate Rossi to claim his third race of the season.
Rossi's second placing allowed him to stretch his lead in the world championship to 38 points over Fiat Yamaha teammate Jorge Lorenzo of Spain, who crashed out of the race on turn one.
The Italian said he drove a careful race after Lorenzo's crash to ensure his team earned vital championship points
"If I made a mistake today after the crash of my teammate it is a big problem," Rossi said. "I tried anyway to win for sure and it was a great race, one of the funniest and most important second places of my career.
"Riding MotoGP at Phillip Island is always a great pleasure and we did some great slides on the left side so it was funny," he said.
Pedrosa secured his first podium finish in the Australian GP MotoGP class, while Alex de Angelis was fourth and American Colin Edwards on a Yamaha was fifth.
Two rounds of the world championship remain - at Malaysia and Valencia - with Rossi on course to claim his seventh world championship.
Italian Marco Simoncelli, riding a Gilera, won Sunday's 250cc race which was halted after Italy's several falls with six of 25 laps remaining. Hector Barbera of Spain was second and Raffaele de Rosa was third.
Spaniard Julian Simon clinched the 125cc world championship when he passed British Aprilia teammate Bradley Smith on the final lap to win by .313 of a second. His victory gave him an unassailable 55.5 point lead over Smith with two championship rounds remaining.
"I'm really, really happy, Simon said. "The race was really complicated and even in the last lap Bradley was pushing a lot."
