third in a row going back to last season by 22.2 seconds from McLaren's Lewis Hamilton.
"Thank you boys, fantastic race. Really controlled, thank you very much. Very cool. Excellent car, excellent stops. We learned a lot today," Vettel said on his team radio after crossing the line.
"It wasn't an easy win, the start was crucial and obviously I got a good getaway," Vettel added in a news conference.
"The second part of the race, Lewis dropped off and I could control the situation a bit better.
"It's the first time I've finished in the Australian Grand Prix so I'm really happy."
Hamilton again paid tribute to McLaren for a remarkable turnaround from a severely disrupted pre-season testing, although he did have to contend with a "massively damaged" floor for the latter part of the race. "In the end. I was just nursing the car home to win the points because we are going to need them over the rest of the season," said the Briton, the 2008 winner here and world champion. "But I think we had good pace out there."
Renault's Vitaly Petrov claimed his and Russia's first ever podium in third place as the top three all ran two-stop strategies, despite the new Pirelli tyres which are supposed to degrade more quickly.
McLaren's Jenson Button had an eventful afternoon after losing two places from fourth on the grid at the start, which effectively ended his chance of winning the race for the third year in a row.
Petrov goes from zero to hero
Vitaly Petrov celebrated his transformation from zero to hero after finishing third in the race on Sunday to become the first Russian to stand on the podium.
The 26-year-old was in danger of losing his drive at Renault after being heavily outscored by his team mate Robert Kubica in his debut season last year and only secured a new deal after a battling sixth place in the season-ender in Abu Dhabi.
With the team robbed of Kubica by the serious injuries the Pole sustained in a rally car crash earlier this year, Petrov carried that form into the opener by claiming his best qualifying position of sixth on Saturday.
Petrov roared past Briton Jenson Button and Fernando Alonso and resisted strong pressure from the Spaniard at the end of the race to deliver a famous result for his team.
"I'm delighted to be here on the podium, especially after the winter we had as a team," he said.
"I made a great start, which was probably the key to my race as it got me ahead of Alonso and Button,” he said.