Rosberg finished 0.3s clear of the world champion, who was the only driver to get within a second of his benchmark time on the supersoft tyre.
Behind the dominant Silver Arrows, Ferrari got the better of Red Bull, with Sebastian Vettel and Kimi Raikkonen marginally quicker than counterparts Max Verstappen and Daniel Ricciardo.
McLaren meanwhile showed more signs of their improving form with Fernando Alonso and Jenson Button seventh and eighth, while Toro Rosso claimed the final two spots in the top ten through Daniil Kvyat and Carlos Sainz respectively.
Alonso had celebrated his 35th birthday by setting the early pace with 1m 18.817s, as Rosberg, Hamilton, Ricciardo, Raikkonen, Verstappen, Romain Grosjean, Valtteri Bottas and Sergio Perez at varying times discovered the lack of grip at Turn 1.
After the first 40 minutes Rosberg was fastest on 1m 17.030s, on soft rubber, from Vettel on 1m 17.409s on supersofts and Hamilton on 1m 17.555s on softs. Raikkonen, Ricciardo, Alonso and Verstappen followed, all on supersofts. The Dutchman, however, reported that his rears were finished after only eight laps.
On supersofts however Rosberg stuck the knife into everyone with 1m 15.517s. From there other drivers improved, but the German was left comfortably out in front.
Elsewhere, rookie Charles Leclerc lapped within three-tenths of Grosjean in the second Haas (1m 18.882s to 1m 18.589s), while fellow substitute Esteban Ocon impressed greatly with 1m 18.981s to Renault partner Kevin Magnussen’s 1m 18.933s.
In terms of incidents, the opening 90-minutes proved fairly uneventful, with Valtteri Bottas’ early spin at the hairpin and Grosjean's half-spin at Turn 9 the only major dramas.