Rosberg, 21 points behind the Briton after 10 of 19 races, had been quickest in both Friday sessions despite an explosive high-speed blowout that triggered a long examination of the tyres.
The German ended the final session before qualifying 0.498 seconds slower than Hamilton, who will be chasing his 10th pole position in 11 races later in the afternoon with the bright morning sunshine set to last.
Ferrari's Sebastian Vettel and Kimi Raikkonen were third and fourth fastest respectively, with the German 0.645 slower than Hamilton's best lap of one minute 48.984 seconds.
Behind them came Mexican Sergio Perez, in a Force India, Red Bull's 2014 winner Daniel Ricciardo and Russian team mate Daniil Kvyat.
McLaren, whose drivers are already sure of starting at the back of the grid after collecting a combined grid drop of 55 places for unscheduled engine changes, had another difficult morning.
Fernando Alonso failed to set a lap time due to a suspected exhaust problem while Jenson Button was 17th fastest and ahead of only the Manor Marussias.
(Editing by Ed Osmond)
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