Rosberg started well from pole and was always in charge of a tactical race, even after Hamilton tried to extend his second stint so that he would have the advantage of fresher soft-compound Pirelli tyres in the losing stages.
After stopping for the second and final time on lap 41, 10 later than Rosberg, Hamilton was 12.5s adrift and quickly reduced that deficit to 6.8s with four laps to run, but then he ran into traffic and Rosberg was able to extend the gap to a comfortable 8.2s by the flag.
Behind the Silver Arrows, Kimi Raikkonen drove a strong race for Ferrari to take third and secure fourth in the drivers’ world championship ahead of countryman Valtteri Bottas, as Sebastian Vettel came up from 15th on the grid to take fourth for the Scuderia. The German started on soft rubber and made a set of supersofts last from the 39th lap.
Sergio Perez realised Force India’s potential with a solid fifth, fending off a consistent challenge from Red Bull’s Daniel Ricciardo. Nico Hulkenberg was unable to do better than seventh in the second Force India. He was nevertheless well clear of Williams’ better placed finisher Felipe Massa. The Brazilian was just able to resist attacks from outgoing Lotus racer Romain Grosjean at the end.
Grosjean, like Vettel, had started on softs after getting a five-place grid penalty for a gearbox change, and used a set of supersofts right at the end to jump Toro Rosso’s Carlos Sainz and Red Bull’s Daniil Kvyat, thus departing the team with two final points which ensured that they stayed ahead of Toro Rosso in the standings.
Sainz’s team mate Max Verstappen had an adventurous race which included a stop to replace hugely flat-spotted tyres and a five-second penalty for exceeding track limits during a tough fight with McLaren’s Jenson Button. The Englishman thus took 12th place ahead of Bottas, who made a poor start and then had his race ruined when he was released into Button’s path during the first pit stops; the Williams needed a new front wing but the Finn also had to serve a five-second penalty.
Marcus Ericsson led Sauber team mate Felipe Nasr home for 14th, as Verstappen dropped from 12th on the road to 16th after stewards added a further 20s to his race time for ignoring blue flags late on.
Fernando Alonso had a horrible race for McLaren; he hit Pastor Maldonado at the first corner and was given a drive-through penalty, but maintained that he had been punted into the Venezuelan’s Lotus by Nasr. He finished 17th.
Will Stevens led Marussia team mate Roberto Merhi home, as Maldonado was the only non-finisher.
Hamilton thus ended his year with 381 points to Rosberg’s 322, with Vettel third on 278 and Raikkonen on 150.
In the constructors’ stakes, Mercedes finished with 703 points to Ferrari’s 428 and Williams’ 257.
The teams now regroup ahead of Tuesday's 12-hour Pirelli tyre test at the Yas Marina Circuit.
WATCH: Rosberg makes it three in a row with victory in Abu Dhabi
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