On a hot, dry day at the Bahrain International Circuit, the 30-year-old German, who leads the embryonic title race after winning the season-opener in Australia, was in charge throughout the 90-minutes session.
Rosberg delivered a best lap in one minute and 32.294 with 20 minutes remaining, having been on top since his first flying lap in opening quarter hour.
Defending world champion Hamilton was second quickest, 0.5 seconds adrift of his team-mate and rival, but 1.3 seconds ahead of third-placed Finn Kimi Raikkonen in the leading Ferrari.
Australian Daniel Ricciardo clocked the fourth best time of the opening session in his Red Bull ahead of team-mate Daniil Kvyat and a determined Nico Hulkenberg of Force India.
On another day of paddock speculation about the future of the sport, and notably how qualifying should be structured, there was an air of relief that the on-track action had started.
Spaniard Carlos Sainz was seventh fastest in his Toro Rosso ahead of his team-mate, Dutch teenager Max Verstappen, and the Haas of Frenchman Romain Grosjean.
Brazilian Felipe Massa was 10th for Williams, just ahead of the second Ferrari of four-time champion Sebastian Vettel.
In the absence of unfit-to-race two-time champion Fernando Alonso, McLaren’s rookie Belgian Stoffel Vandoorne was 18th fastest.
Alonso remained in Bahrain after failing a medical on Thursday and helped give advice to his deputy, who had arrived following an overnight flight from Japan.
His time was just less than a second slower than that of McLaren team-mate Jenson Button, a solid effort on his first day in Formula One.
Button, the 2009 champion, was 14th.
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