The German, runner-up in a championship already won by Hamilton, lapped with a best time of one minute 41.983 seconds under the Yas Marina floodlights.
Hamilton, winner in Abu Dhabi last year after Rosberg secured pole position, had been quickest in the afternoon session by 0.141 with a time of 1:43.754 but ended the day 0.138 slower.
Organizers are also making much of the connection between the number 44 on Hamilton's car and the 44th National Day anniversary next week of the founding of the United Arab Emirates.
Another victory would also be the 44th of the Briton's career and he is determined to end the year on a high. So is Rosberg, who is chasing his third successive win and sixth pole position in a row.

Rosberg's car in second practice session at the Yas Marina racetrack in Abu Dhabi
The Mercedes duo, who will also be chasing a record 12th one-two of the season in Sunday's race, were comfortably ahead of the rest.

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