Vettel won by almost 10 seconds from Hamilton and Mercedes team-mate Valtteri Bottas in a commanding victory of tactics and superior speed around the Albert Park street circuit.
Ferrari hadn't won in Melbourne since Kimi Raikkonen's 2007 victory and it was Vettel's second triumph in Australia after winning the 2011 race with Red Bull.
It was also a major fillip for the fledgling season and the new generation of quicker cars after Ferrari's superior pre-season test times as they chase their first world constructors' title since 2008.
- 'Bit of luck' -
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"A title challenge is a long way ahead. For now we are just over the moon at the start we have made here today," Vettel said. "I was not entirely happy with my start, there was a bit of wheel spin, but I was trying to keep the pressure on to give the message that we are here to fight.
"There was a bit of luck that Lewis came out in traffic."
Hamilton's early stop meant he rejoined behind the Red Bull of Max Verstappen which allowed Vettel to open up a decisive gap at the head of the field.
"A big congratulations to Ferrari and Sebastian," Hamilton said. "In the race, I struggled with the tyres. I had to stop very early and I got stuck behind one of the Red Bulls, but that's just the way it goes."
Ferrari's Kimi Raikkonen was fourth with Verstappen fifth ahead of Brazilian Felipe Massa in the Williams.
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