Hamilton had initially been fastest on the hard Pirelli with 1m 40.552s, but on the mediums Rosberg seized the initiative with a blistering lap of 1m 39.008s.
Hamilton, who also experienced a problem with his F1 W05’s seat, responded with a 1m 39.240s that left him 0.232s adrift.
The Mercedes drivers’ laps redefined the ante after Kimi Raikkonen had gone fastest as the first runner to use the mediums, with a lap of 1m 40.156s for Ferrari.
That held up for third best as Sebastian Vettel, who did not run until the second half of the hour-long session, posted a late 1m 40.387s for Red Bull. Mercedes, Ferrari and Red Bull all looked strong on differing parts of the track, but the Renault-powered cars from Milton Keynes still lack straight line grunt.
Nico Hulkenberg again excelled for Force India with fifth fastest time of 1m 40.523s, which put him ahead of Red Bull's Daniel Ricciardo on 1m 40.686s and Ferrari's Fernando Alonso on 1m 40.736s. Felipe Massa was Williams’ faster runner in eighth, with his1m 40.781s just enough to shade team mate Valtteri Bottas’s 1m 40.891s, as the FW36’s rear end continued to disappoint.
Sergio Perez rounded out the top 10 for Force India with 1m 41.029s, while Daniil Kvyat headed Toro Rosso partner Jean-Eric Vergne, 1m 41.182s to 1m 41.441s. Adrian Sutil was the final runner below 1m 42s, with 1m 41.552s. His Sauber stable mate Esteban Gutierrez managed 1m 42.041s.
Lotus had a much better day than yesterday, with both E22s running all through the session. But 15th fastest Romain Grosjean rubbished the rear-end performance after posting 1m 42.749s to head Pastor Maldonado on 1m 43.539s, and their numerous off-track moments attested to the car’s current shortcomings.
Max Chilton again headed the sickly Jules Bianchi after taking his Marussia round in 1m 43.977s to the Frenchman’s 1m 44.170s, while Marcus Ericsson edged troubled Caterham team mate Kamui Kobayashi with 1m 44.457s to 1m 46.015s.
McLaren? They had a difficult session, with numerous problems including loss of engine power for Kevin Magnussen - which nearly resulted in him being collected by Massa.
The Dane was unable to set a time and propped up the bottom of the time sheet as a result, directly below Jenson Button, who set an unrepresentative 2m 05.555s.