No Formula One team had won on their debut since Wolf in 1977 while the last to secure the top two places first time out was Mercedes [ Images ] in 1954.
McLaren's [ Images ] world champion Lewis Hamilton [ Images ], who started 18th after a catastrophic gearbox failure in qualifying, showed all of his fighting spirit by clawing his way back to fourth place.
The 29-year-old Button led from pole to chequered flag at Albert Park, taking his first victory since Hungary in 2006 and scoring more points in a single afternoon than he had in the previous two seasons with Honda.
Brazilian team mate Rubens Barrichello [ Images ] started and finished second but only after Red Bull's Sebastian Vettel [ Images ] and BMW-Sauber's Robert Kubica [ Images ] collided three laps from the end while second and third respectively.
That brought out the safety car for the closing laps before it came in at the final corner.
Germany's [ Images ] Timo Glock [ Images ] was fifth for Toyota ahead of Renault's [ Images ] Fernando Alonso [ Images ] and Williams' Nico Rosberg [ Images ]. Toro Rosso's Swiss rookie Sebastien Buemi [ Images ] became the 58th driver to score on his debut with eighth place.
Button, written off as an overpaid has-been when Honda decided in December to pull out, completed an astonishing comeback that ensured he will never again be regarded as a one-hit wonder.
"Sensational job. Fantastic. Well done, you deserve it," team principal Ross Brawn [ Images ] told Button over the team radio after he crossed the line.
"Thank you, you are all legends. It's going to be a great year," replied Button.
The first race of a new-look Formula One, with radically-revised aerodynamic regulations, slick tyres and the new KERS energy recovery systems, turned the starting grid upside down and shook up the pecking order as many had predicted.
Neither of the Ferraris finished, with Felipe Massa [ Images ] retiring on the 46th lap and 2007 world champion Kimi Raikkonen [ Images ] following him out. Hamilton's Finnish team mate Heikki Kovalainen [ Images ] retired after being caught in a first lap coming together.