Once Vettel overtook Perez, it was only a matter of time before Webber would be forced to change tires and relinquish the lead. Webber eventually entered the pits for his first tire change to soft tires on the 29th lap.
Vettel made his second and last stop on the 32nd lap to take on new medium tires, returning to the track just over eight seconds behind Webber.
Webber failed to make up enough time on the soft tires before switching back to mediums two laps later, effectively handing the race to Vettel.
“I’m not that old yet, I have goals, maybe in 10 years’ time, I’ll understand what we have done,” Vettel said.
Red Bull ordered a stunned Webber to stop while in second place on the 42nd lap due to a problem with his car’s alternator.
“Disappointing, but there’s not much I can do,” Webber said. “There was something wrong with the car, so we had to stop straight away.”
With the Australian out, the race became a tussle for the lesser podium places, with pacesetting Rosberg passing Lotus driver Kimi Raikkonen for second on the closing laps.
Grosjean drove a dogged race to defy the odds and reach the podium after being eliminated in the first qualifying session Saturday.
“The car came back in the race, our strategy was good,” he said. “It was tough, I’m very proud.”