The Englishman, who leads the world championship by 17 points, set the pace initially, had a spell when Jenson Button was quickest in the fast-improving McLaren, then took back the initiative with a lap of 1m 39.941s. Rosberg's response was 1m 40.223s, as Button stayed a very respectable third on 1m 40.319s.
There was then a bit of a gap back to fourth-placed Daniil Kvyat in the Toro Rosso on 1m 40.887s, the Russian just ahead of Kevin Magnussen, who confirmed McLaren's recent upturn in performance with 1m 40.987s.
Fernando Alonso was sixth for Ferrari with 1m 41.065s, ahead of Sebastian Vettel in the lead Red Bull on 1m 41.463s. The world champion will use an entirely new power unit this weekend - his sixth of the season - and is therefore likely to start Sunday's race from the pit lane, once a penalty is applied.
Behind Vettel, Felipe Nasr did a good job for Williams, going eighth-fastest with 1m 41.545s, as Nico Hulkenberg took his Force India round in 1m 41.722s to pip Toro Rosso rookie Max Verstappen on 1m 41.785s. Felipe Massa recorded 1m 41.907s in the other Williams, whilst Kimi Raikkonen lapped in 1m 41.965s to take 12th in the second Ferrari.
Pastor Maldonado had a slightly wild half spin at the end in his Lotus but was 13th on 1m 42.329s ahead of another spinner - Adrian Sutil, who took his Sauber round in 1m 42.333s.
Sergio Perez was 15th fastest for Force India on 1m 42.459s, just ahead of fellow Mexican Esteban Gutierrez who lapped in 1m 42.516s in the second Sauber. The final two spots on the timesheet went to Daniel Ricciardo, who struggled to 1m 42.598s before encountering technical problems with his Red Bull, and Romain Grosjean who lapped in 1m 43.229s, but looked uncomfortable in his Lotus throughout.
Overall, it was a relatively undramatic 90 minutes, as the teams focused on tyre evaluation.