Kimi Raikkonen held off Ferrari's Fernando Alonso of Spain and German Red Bull world champion Sebastian Vettel at the chequered flag.
It was the 33-year-old Raikkonen's 20th GP win and follows his triumph in the 2007 Australian race on his way to winning the world drivers' title when driving for Ferrari.
Raikkonen coasted to the finish line and beat Alonso by 12.4secs with Vettel a further 9.8secs away in third.
"Thanks everybody, I told you that the car is good," Raikkonen said over his team radio as he returned to pits.
Alonso's Ferrari teammate Felipe Massa of Brazil was fourth with Britain's Lewis Hamilton in a Mercedes fifth and Australian Mark Webber in a Red Bull sixth.
Raikkonen won the race despite only coming into the pits for two tyre changes compared to three employed by his rivals.
Eighteen cars finished the 58-lap race around the Albert Park street circuit with two retirements by Nico Hulkenberg and Daniel Ricciardo, while Nico Rosberg and Pastor Maldonado both encountered car trouble on the circuit.
The second race on the F1 circuit will be at Sepang in Malaysia next weekend.