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The 30-year-old began the race on the front row alongside teammate Nico Rosberg and took the lead in the first lap when the German slipped to fifth place, although Rosberg regained his advantage after Hamilton's second pit stop.
Rosberg appeared to be heading towards victory with 10 laps remaining, but a safety car halted the 30-year-old's progress.
The German continued to lead as the track was cleared for racing, but an error saw the 30-year-old run off track, allowing Hamilton to overtake his teammate.
Rosberg closed down his opponent in the race's final laps, but Hamilton held off the challenge to secure his third Formula 1 championship title.
Vettel's teammate Kimi Raikkonen was one of eight drivers who did not finish the race, as the Finn damaged his brakes after going off track.
1. Lewis Hamilton (Mercedes)
2. Nico Rosberg (Mercedes)
3. Sebastian Vettel (Ferrari)
4. Max Verstappen (Toro Rosso)
5. Sergio Perez (Force India)
6. Jenson Button (McLaren)
7. Carlos Sainz (Toro Rosso)
8. Pastor Maldonado (Lotus)
9. Felipe Nasr (Sauber)
10. Daniel Ricciardo (Red Bull)
11. Fernando Alonso (McLaren)
12. Alexander Rossi (Manor)
Did not finish: Daniil Kvyat, Nico Hulkenberg, Marcus Ericsson, Kimi Raikkonen, Felipe Massa, Romain Grosjean, Valtteri Bottas, Will Stevens