The 26-year-old German, who claimed his maiden victory in last weekend’s Chinese Grand Prix and was fastest in Friday practice, remained the fastest man as he delivered a best lap of one minute 33.254 seconds early in an hour-long session that he dominated.
This meant he comfortably topped the times by 00.10secs ahead of defending double world champion compatriot Sebastian Vettel of Red Bull after enjoying a half-second advantage at the head of the field for most of the morning.
Vettel, who had struggled with over-heating problems during the session, delivered his best lap in the final minutes and in the most favourable track conditions on another hot and dusty day at the Sakhir circuit.
That lifted him up to second ahead of his Red Bull team-mate Australian Mark Webber and pushed championship leader Briton Lewis Hamilton, the 2008 champion, down to fourth in his McLaren.
Seven-times champion German Michael Schumacher, 43, was fifth fastest in the second Mercedes after struggling with severe tyre-wear problems, ahead of Briton Jenson Button, the 2009 champion, in the second McLaren.
Another champion, Finn Kimi Raikkonen, who won the title in 2007 for Ferrari, was seventh for Lotus ahead of Australian Daniel Ricciardo of Toro Rosso, Frenchman Romain Grosjean in the second Lotus and two-time champion Spaniard Fernando Alonso of Ferrari.
All of the teams struggled with tyre-wear problems in the heat with sand and dust blowing across the circuit - conditions that suggest a minimum three-stops strategy for Sunday afternoon’s race.
Pirelli motorsport director Paul Hembery said: “The teams are all suffering with degradation - on the soft tyre it’s about two-tenths per lap.
“I think they’ll qualify on the soft tyre and the vast majority will do a three-stop strategy, moving onto the medium tyre in the race.
“McLaren are doing a lot of work on the soft tyre to see if they can maybe take a sprint approach with the compound in the race. Let’s see.”
Hamilton said of Rosberg and Mercedes: “It looks as if they have cracked it now with that car. It’s really fast. It’s at least as good as us now!”
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