Hamilton, who needed Rosberg to finish below third in the race to become the world champion, drove deliberately slowly, defying team orders, in an attempt to bring other drivers into the battle.
Rosberg was under pressure from Sebastian Vettel but managed to hold the Ferrari driver to claim the second spot. Max Verstappen came in fourth, Daniel Ricciardo followed his Red Bull team-mate in fifth.
Ferrari's Kimi Raikkonen was sixth ahead of Force India's Nico Hulkenberg and Sergio Perez, helping Force India easily secured their fourth position in the constructors' championship. Williams' Felipe Massa and McLaren's Fernando Alonso completed the top 10.
Rosberg kept his cool throughout the race despite the pressure from Vettel, but said it had been tough.
"That definitely wasn't the most enjoyable race I've ever had!" he admitted after the race, as quoted by www.formula1.com.
"With Max early on, and then with these guys coming at the end, it definitely wasn't fun. I'm just really glad it's over!"
Hamilton shook hands with Rosberg, who dethroned him as the F1 champion, and they hugged on the podium. "Winning the championships is a great feeling," Hamilton said as he congratulated his team mate, "and I'm looking forward to fighting with him for it again next year."