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.
Hamilton on pole for season-opening Australian GP
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.
That winning feeling for @ScuderiaFerrari and Sebastian Vettel ๐ ๐ป ๐#AusGP #F1 pic.twitter.com/t2DKaVY8TK
— Formula 1 (@F1) March 26, 2017
The victory was the German four-time world champion's fourth for Ferrari and his first since Singapore in 2015 and his 43rd career win.
"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."
"I could control the race" - #AusGP race winner Sebastian Vettel #F1isBack pic.twitter.com/8Ld8Mehbpm
— Formula 1 (@F1) March 26, 2017
Ferrari got the better of Mercedes in the sole round of tyre changes which ultimately decided the race.
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.
Hamilton pips Vettel in first-day testing
"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."
"I'll be coming back stronger in the next race, that's for sure" ๐ช
— Formula 1 (@F1) March 26, 2017
Fighting talk from @LewisHamilton after his P2 finish today#AusGP ๐ฆ๐บ pic.twitter.com/i2gW5yNflx
Ferrari's Kimi Raikkonen was fourth with Verstappen fifth ahead of Brazilian Felipe Massa in the Williams.
Australia's big hope Daniel Ricciardo had a heartbreaking day with gear box problems ending his race on the 29th lap after he was forced to start from pit lane when his Red Bull car broke down on the warm-up lap.
Hamilton, who went into the race on his fourth successive pole in Melbourne, got away safely and avoided trouble into the notorious right hander out of home straight.
But Kevin Magnussen in a Haas clipped the kerb and slid into the Sauber of Marcus Ericsson on the first turn. Both cars continued on in the race.
Hamilton grabbed a 1.5sec gap on Vettel after nine laps ahead of Bottas, Raikkonen and Verstappen.
Hamilton made his first pit stop after lap 17 to change to soft tyres on his Mercedes to hand the lead over to Vettel and rejoined the race in fifth spot behind Verstappen.
"Race critical that you pass Verstappen," Hamilton was told over the team radio to which he testily responded "how do you expect me to do that right now?" as his pace slowed behind the Red Bull.
Vettel came into the pits to change tyres and rejoined the race just squeezing in ahead of Verstappen and Hamilton.
When Verstappen came into the pits Vettel had opened a six-second lead over Hamilton at mid-distance.
Ricciardo's traumatic race came to a sorry end on the 29th lap with his Red Bull coming to a stop with lingering gearbox problems.
Bad news: 24 hours to forget for @danielricciardo in ๐ฆ๐บ
— Formula 1 (@F1) March 26, 2017
Good news: You can put it right in two weeks ๐จ๐ณ#AusGP pic.twitter.com/OJrspiVv8I
"Sorry mate - the car's done," the Red Bull team told the disconsolate Ricciardo over the radio.
Vettel extended his lead over Hamilton to over nine seconds after 41 laps with the triple world champion seemingly unable to reel him in.
Bottas was pressuring Hamilton and was only just over two seconds behind in third place with Raikkonen struggling in fourth place ahead of Verstappen.
Mercedes had no answer to the pace of Vettel, who posted a new fastest lap of 1:26.638 in the final laps of the race.
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