Former Formula One world champion Hamilton overcame mechnical problems in the first session to top the charts just ahead of his German team-mate Rosberg.
Rival drivers have tipped the Mercedes pair to fight it out for Sunday's race, given the team's superior pre-season testing and adjustment to sweeping technical changes.
A return to turbocharged engines, lower fuel loads, gearbox changes and new energy recovery systems are among significant rule changes for the new season.
Hamilton put in a scorching lap on soft tyres to post a best time of one minute 29.625, some 0.157secs ahead of Rosberg (1:29.782).
Ferrari's Fernando Alonso backed up from topping first practice with the third best time of 1:30.132, just over a half-second slower than Hamilton.
Four-time world champion Sebastian Vettel was fourth quickest in his Red Bull in 1:30.381, but a significant 0.756secs down on Hamilton.
It wasn't so enjoyable earlier in the day for Hamilton, the 2008 world champion, who came to a halt on his installation lap in the first practice session.
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