Hamilton's victory cut his deficit to Ferrari's Sebastian Vettel to just one point in the championship as the German suffered a front-left tyre failure when running third with two laps to go, dropping to seventh.
The same problem had hit Vettel's team-mate Kimi Raikkonen the lap before, costing the Finn an almost certain second place, promoting Hamilton's team-mate Valtteri Bottas to a Mercedes one-two. Raikkonen recovered to finish third.
Following the podiums celebrations, Hamilton went down to see the crowd, surfing on their outstretched hands and high-fiving as he ran past the adoring throng.
"The support has been incredible this weekend," he said. "I am so proud I could do this for you all. Now the plan is to win the championship."
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