The 30-year-old German, who has produced remarkable dominant form since seeing Hamilton secure his third drivers' title at last month's United States Grand Prix, made a perfect start from his sixth successive pole position and, pit-stops apart, was in control all the way.
Rosberg was celebrating his sixth win of the year and the 14th of his career. It was his first success at the Yas Marina circuit where Hamilton beat him in 2014 to take his second title.
Finn Kimi Raikkonen finished third ahead of his Ferrari team-mate, four-time former champion Sebastian Vettel and Sergio Perez of Force India.
Daniel Ricciardo was sixth for Red Bull ahead of Nico Hulkenberg in the second Force India, Felipe Massa of Williams, Romain Grosjean who marked his last race for Lotus with a surge to ninth and Daniil Kvyat in the second Red Bull.
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The race was preceded by an announcement from the stewards that cleared Ferrari and the American Haas team, which is set to join the grid next year, of any wrong-doing in their joint use of the Ferrari wind-tunnel to prepare cars.
This announcement clarified the issues and closed a possible loophole, leaving the paddock to focus on the final contest in perfect sunset conditions with a track temperature of 29 degrees Celsius and the two Mercedes together again on the front row.
When the lights went out, Rosberg made a perfect start while Hamilton struggled to stay with him and had to engage his best defensive driving to retain second place.