Hamilton then took the lead after 29 laps as Rosberg retired with gearbox failure.
Hamilton came home 30 seconds clear of Finn Valtteri Bottas of Williams, who started 14th. Australian Daniel Ricciardo of Red Bull finished third ahead of Jenson Button, the 2009 champion, of McLaren and defending four-time champion Sebastian Vettel in the second Red Bull.
It was Hamilton's fifth win this year, his second in his home event and the 27th of his career.
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