Valtteri Bottas was third fastest for Mercedes behind the two Ferraris, but ahead of his team-mate Lewis Hamilton who has a five-place grid penalty after an overnight gearbox change and starts from ninth.
Daniel Ricciardo set the fifth fastest time, the lone Red Bull in Q3 after his team-mate Max Verstappen crashed out during Q1, albeit with a time that prevented him being knocked out in the first session.
Sebastian Vettel, victor at Australia and last 12 months in Bahrain, was fifth quickest ahead of past season's pole-sitter Valtteri Bottas who was first sixth for Mercedes.
Bottas was closing the gap on Vettel as his tyres faded and closed to within two seconds of the German going into the final laps.
There would be light contact between the Mercedes and Red Bull, however, with the Dutchman picking up a puncture, at the same time up ahead, his teammate Daniel Ricciardo was pulling over to the side of the track after his auto shutdown.
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Red Bull's race unravels early: Red Bull's race went south pretty quickly.
Hamilton had been poised to win at Albert Park only for a timing error on the Mercedes pit wall during a virtual safety auto period to gift-wrap the victory to his rival Sebastian Vettel.
Verstappen's vehicle lost power and stopped on the track in the first session. Raikkonen was given the green light to go but it was an unsafe release and, as he pulled away, his auto hit one of the mechanics. But that came courtesy the timely deployment of the virtual safety vehicle with Hamilton, until then, set to wrap up a comfortable victory in his Mercedes which had a clear edge over Vettel's Ferrari all weekend.
The story of the race changed in the pit-stop phase when Ferrari pitted both cars ahead of both Mercedes, with Hamilton going longer on the Soft tyre. The Finn immediately stopped in the pit lane and jumped out, while the injured mechanic was taken to the medical center for a full check. The team subsequently tweeted that he had been transported to a nearby hospital for further treatment.
Raikkonen topped the leaderboard just ahead of Ferrari teammate Sebastian Vettel by 0.011 seconds.
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Vettel said after the race he had nothing left from his tyres - Bottas did not seem to fully commit to the opportunity for a late lunge at the start of the final lap.
This left Hamilton to make up places and after slipping to 10th he regained ninth and then passed Alonso, Hulkenberg and Ocon in one move.
It was Vettel's 49th career victory on the occasion of his 200th race start and importantly, with his second win of the season, he extended his world championship lead over Hamilton to 17 points.
There were also celebrations at Sauber, with Sweden's Marcus Ericsson finishing ninth for his first points since 2015 and the Swiss team's first of the season, but gloom at Williams whose drivers finished last.
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As a result, Vettel had to complete 39 laps on one set of soft tyres while Bottas' strategy meant he had the more durable medium compound to complete 37 laps to the flag after his pit stop.