The 30-year-old Briton, who started from second on the grid on Sunday, came home 2.850 seconds clear of his Mercedes team-mate Nico Rosberg to deliver his 10th victory of a dominant season.
Hamilton now has an unbeatable total of 327 points, moving him beyond the reach of both Rosberg, who finished second, and four-time champion Sebastian Vettel of Ferrari, who came home third.
But an emotional Hamilton owed his victory, in the end, to an unforced error by Rosberg on the 49th lap when he made a mistake and ran wide at Turn 15 as the pair duelled for the lead.
"Thank you all so much, I am so grateful to you all. And to my family I love you all."
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Dutch teenager Max Verstappen finished fourth for Toro Rosso ahead of Sergio Perez of Force India, Carlos Sainz in the second Toro Rosso, Jenson Button of McLaren and Pastor Maldonado who was eighth for Lotus.
Felipe Nasr came home ninth for Sauber and Australian Daniel Ricciardo was 10th for Red Bull, having passed two-time champion Fernando Alonso of McLaren on the final lap.
Hamilton's success enabled him to equal the record of Jackie Stewart as the only Britons to win three drivers' world titles and the first to win two championships in succession.
"Something like that (his late error) has never happened to me ever. Really tough to lose the lead and the win like that."
Vettel, who started from the middle of the grid after a 10-place penalty, added: "We have a great car. I think we have exceeded all expectations, but it doesn't feel great when you cross the line and you know you can't win the championship any more."
After a two-day deluge, the race began with a rare appearance by the sun, a drying breeze and all the drivers on intermediate tyres.