After his planned first pit stop, Vettel found himself behind Hamilton, and delayed by dirty air, could not get past the Brit until early on lap 26, after which Hamilton pitted for medium tires, on which he would finish the race.
Vettel hung on ahead of the charging Mercedes on the final lap to take his second win in two races this season and one of the best of his illustrious career.
With further stops required, Ferrari's problems were compounded after 36 laps when Raikkonen came in and inadvertently ran over a mechanic as he pulled away.It was his second unsafe release of the weekend and his third in a race.Unaffected, Vettel pushed to make the most of an emergency one-stop strategy, resisting Bottas all the way to the flag.
Mercedes appeared to be readying to pit Bottas, but changed their minds when Vettel made his pit stop ahead of them on lap 18, with 39 to go, the Ferrari fitting soft tyres.
Ferrari was also fined 5,000 euros ($6,140) for the same error during practice on Friday. He was left with a rear left puncture and limped back to the pits for new tyres before retiring the auto due to damage from the early incident.
"I came on the radio to say everything was under control, but that was a lie!" Hamilton, out of position on the grid following an unscheduled gearbox change, failed to make any ground on the opening lap before losing a place to Fernando Alonso. The Kiwi had been handed a ten second penalty by the race stewards for causing a collision and now found himself circulating in 16th place ahead of the two Williams of Stroll and Sergey Sirotkin.
Ahead of him was Nico Hulkenberg in sixth place for Renault F1 and Kevin Magnussen fifth for Haas-Ferrari, confirming both Haas' pace shown in Australia and also how incredibly tight the midfield battle is. The podium was completed by Bottas and Hamilton, in that order. "I began ninth so third is not risky in any respect". By them going onto the medium, I thought: 'That's checkmate.' Because we had to come in again. I really tried to keep it as clean as possible. I had to nurse the tyres. "Our plan worked but just, Bottas had a bit of a sniff but ran out of laps", said the four times champion.
"I am sorry for Kimi who could certainly have finished on the podium", he added. Firstly congratulations to Sebastian and Valtteri did an exceptional job.
The Briton was hampered by radio issues throughout the race and sounded frustrated during communications with his crew.
The racing continued to flow, with Hamilton in the thick of it.
Vettel, needing to open a gap over Hamilton, caught him on lap 25 and was through to retake the lead a lap later.