The German, starting from third behind his Ferrari teammate Kimi Raikkonen and Hamilton on pole, took the lead when he pitted while the virtual safety car was out following Romain Grosjean's retirement after a failed tyre change, reports Efe.
"We got a bit lucky obviously with the safety car, but I really enjoyed it. I was hoping my start would be a bit better", Vettel said.
"I was praying for the safety car", the four-time world champion added.
While Hamilton's speed was limited due to the VSC, Vettel's in the pitlanes was not, allowing him to come out ahead of the Briton in first position.
Hamilton, suddenly finding himself in second place, was not able to get close enough to trouble Vettel, despite having the best overall pace.
The clean air in front of Vettel and the turbulent air behind him kept Hamilton at bay, and despite starting from pole position and not making any major errors, the Mercedes man was forced to settle for second behind the German's Ferrari.
"Today they just did a better job", Hamilton said. "This is one awesome circuit, but it's so hard to overtake. At the end we were just trying to live to fight another day."
The result will be good news for fans hoping for a more unpredictable season and a challenge to the dominance shown by Mercedes over recent years.
The German team has won the last four world championships, with Lewis Hamilton winning three of them.
An uneventful start had meant the top three drivers maintained their starting positions, and Hamilton held off an early challenge from Raikkonen in second place, before he began to open up a gap.
Haas' Magnussen overtook Verstappen on turn one in the only change to the top of the leaderboard.
The top three began to open up a gap ahead of Magnussen, whom Verstappen could not get past.
The Dutchman let his frustration get the better of him when he spun at turn 1, dropping three places as his teammate Ricciardo, Grosjean in the other Haas and Nico Hulkenberg overtook him.
With no crashes at the start and overtaking difficult at Albert Park, the race quickly became about pit strategy.
Raikkonen pitted on lap 18, with Hamilton following a lap later, allowing Vettel into first place, who tried to extract as much as he could from the tyres he started with and open up a gap on Hamilton in second before his crucial pit stop.
Magnussen's race was over after a tyre change went wrong on lap 23, a hugely disappointing end after such a promising start from the Dane.
Haas' day soon got worse as Grosjean crashed out after another failed tyre change.
The virtual safety car came out and Vettel pitted, taking advantage of the temporarily limited race speed to come out ahead of Hamilton and retain the lead, which he would not relinquish.
Despite a late push against Kimi Raikkonen's Ferrari from Daniel Ricciardo, the Red Bull man was unable to give the home fans a first ever podium finish from an Australian driver.
Fernando Alonso produced an excellent result in his McLaren, raising hopes that the team might be about to enter a more fruitful and successful era after their recent troubles.
The Spanish two-time world champion surged from 11th to finish in 5th, ahead of Max Verstappen's Red Bull in sixth.
While Ferrari, and Vettel in particular, can count themselves lucky, they showed enough pace to suggest they will push Mercedes all the way this year.
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
