While Rosberg set the fastest lap of the day in the morning session, with a lap of one minute 26.828 seconds, Hamilton was comfortably quicker in the afternoon sunshine at the Circuit de Catalunya.
The Briton's time of 1:26.852 compared to Rosberg's 1:27.616, although the German had gearchange problems, as the sport fired up for its first European weekend of the season.
Rosberg was summoned to the stewards, including former world champion Alan Jones, after first practice for a pitlane infringement.
Force India's Mexican Sergio Perez was then fined 1,000 euros (£728) for speeding in the pit lane during the second practice.
Hamilton, last year's winner in Spain, has won three of four races this season and started all on pole. He leads Rosberg by 27 points.
Ferrari's Sebastian Vettel was third and second fastest in the sessions, but still some way off the Mercedes pace, with team mate Kimi Raikkonen fourth in both.
Toro Rosso's rookie pairing of Carlos Sainz, making his home debut, and Max Verstappen were in the top 10 in both sessions but Red Bull had a difficult day.
Australian Daniel Ricciardo was sidelined for much of the two sessions while the team worked on his car's engine.
Ricciardo, who is already on his fourth engine for the season out of an allocation of four, ended up ninth and 13th.
Frenchman Romain Grosjean brought out red flags when the engine cover of his Lotus blew off and shattered into pieces on the pit straight.
Susie Wolff made the third practice appearance of her career with Williams, 40 years on from the only occasion on which a woman driver has finished in the points, and ended up with a faster time than two world champions.
The Scot, who will not race on Sunday, was 14th fastest and ahead of McLaren's Fernando Alonso and Jenson Button -- 15th and 16th respectively. Valtteri Bottas then took the car back for the afternoon and was eighth fastest.
Double champion Alonso was returning to the home circuit where he crashed heavily in pre-season testing, an accident that forced him to miss the Australian season-opener. He was an encouraging 11th in the afternoon.
(Editing by Ed Osmond)
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