Button survived an incident-filled race at Melbourne's Albert Park to convert pole position into just his second Grand Prix victory in 154 starts. The 29-year-old was never headed in the 58-lap race, beating team-mate Rubens Barrichello and Toyota's Jarno Trulli.
Reigning world champion Lewis Hamilton finished fourth in his McLaren.
The race finished behind the safety car after Red Bull driver Sebastian Vettel and BMW-Sauber's Robert Kubica first collided, then crashed separately, when running second and third respectively with three laps remaining.
Australian Mark Webber had a nightmarish start to his home town race.