The Mercedes W05 was clearly the fastest car on both of the available tyre compounds as both Rosberg and Lewis Hamilton led the times during early running on mediums.
Rosberg was the first to lap under 1m30s after swapping to softs, lowering the bar to 1m29.375s, and while Hamilton was fastest of all in the first sector in response, he lost time in the middle sector to end the session fourth quickest, 1.501s off Rosberg's best.
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Even though there were spots of rain before the green flag and it was generally cloudier than yesterday, with a gusting wind, the top runners quickly got into the groove and began to improve their times.
Button reported a litany of imperfections in his McLaren's performance, from locking rear brakes to poor balance on corner entry and exit. But on soft tyres at the end he found enough speed to go second fastest overall, just over a tenth of a second quicker than Ferrari's Fernando Alonso.
The Spaniard was the most assured of the Scuderia's drivers, lapping comfortably while team-mate Kimi Raikkonen ran off-track more than once as he struggled with his car's balance and finished the session 1.7s off the ultimate pace.
Daniel Ricciardo was quickest of the Red Bulls with 1m30.970s, accomplished on the soft tyres, but Sebastian Vettel was a full 2.880s off Rosberg's best and finished final practice complaining of a lack of acceleration.
Williams had a less positive session than yesterday, with Felipe Massa propping up the top 10 and Valtteri Bottas completing just two untimed laps before parking his FW36. He will incur a five-place grid penalty after the team confirmed it would have to change his car's gearbox.
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Those teams whose new cars are in a less mature state of development continued to struggle. Esteban Gutierrez returned to the Sauber garage after reporting a gearbox problem and sat out the remainder of the session.
Both Lotus and Marussia had to use one of their six permitted 'jokers' to break the curfew on garage working hours, but they, along with Caterham, at least ran more laps than yesterday.
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