Polesitter Hamilton controlled the race on the Albert Park street circuit to win from teammate Nico Rosberg of Germany.
Four-time world champion Sebastian Vettel took the final podium position for his new team Ferrari, holding off Felipe Massa in the Willams.
It was the 34th career victory for two-time world champion Hamilton and underlined the continued dominance of Mercedes as he and Rosberg pulled well clear of their nearest challengers.
Hamilton, who was forced to retire early in last year's Australian Grand Prix, was taking the checkered flag in Melbourne for the first time since 2008, when he claimed his first world title for McLaren.
It had all gone completely to plan until coming face to face on the victory podium with movie legend Arnold Schwarzenegger, who was conducting the post-race interviews.
"Hey man, WOW," said a surprised Hamilton.
"It is an incredibly feeling to continue winning but also great to be up here with you." Then taking his courage in his hands, Hamilton cheekily told 'The Terminator' "I thought you were taller!"
After getting the thoughts of Rosberg and Vettel, who said it was a "very big honor" to gain his first points for Ferrari, Schwarzenegger turned his attention back to Hamilton.
The pair signed off by saying together: "I'll be back," the catchphrase from Schwarzenegger's iconic 1984 film.
With Hamilton winning his seventh race from eight starts, his F1 rivals would probably rather he stayed away and Rosberg admitted "he was driving to his max" but could not match the pace of his teammate.
Only 11 cars finished the race from a depleted grid of 15 cars, with Valtteri Bottas unable to start for Williams due to a back injury.
Pastor Maldonado crashed out on the first lap as the safety car was deployed, while his teammate Romain Grosjean retired early in the 58-lap race to complete a miserable afternoon for Lotus.
Britain's Jenson Button in an uncompetitive McLaren was the only driver to finish without a point in 11th place.
His regular teammate Fernando Alonso sat out the race after his nasty crash in pre-season testing in Barcelona, while stand-in Kevin Magnussen retired after the warm-up lap.
Kimi Raikkonen looked set to underline Ferrari's improvement when running in fifth place, but had to retire the car, with TV replays indicating his left rear tire was not fitted properly after a pit stop.
It left the way clear for rookie Felipe Nasr of Brazil to claim an unexpected fifth place for Sauber, which went through the 2014 season without claiming a single point, and also took eighth spot with Marcus Ericsson.
Home hopes rested with Daniel Ricciardo, third in last year's title race, but he looked off the pace in the Red Bull in sixth place.
Force India pair Nico Hulkenberg and Sergio Perez finished seventh and 10th, with Carlos Sainz Jr. impressing on his F1 debut for Toro Rosso in ninth.
Dutch teenager Max Verstappen made F1 history by becoming the youngest driver to compete in an F1 race at 17 years and 166 days, but his hopes were dashed when forced to retire in his Toro Rosso on the 34th lap.