With the circuit bathed in sunshine, rather than sodden as was the case on Thursday, Rosberg generally had the upper hand throughout the 90 minutes, setting the best time of 1m 35.461s to Hamilton's 1m 35.612s.
Hamilton, who captured the points lead from Rosberg following his triumph in Singapore, had a couple of minor offs exiting the second of the Degner Curves, but appeared to have very strong race pace during longer run simulations.
Ferrari's Fernando Alonso was their closest pursuer on 1m 36.037s, 0.727s adrift of Rosberg, while team mate Kimi Raikkonen set the fifth fastest time despite finishing one second further down the road, on 1m 37.187s. They were separated by Valtteri Bottas who took his Williams round in 1m 36.576s.
Kevin Magnussen took sixth for McLaren on 1m 37.327s ahead of Daniel Ricciardo's Red Bull on 1m 37.466s, Jenson Button in the second MP4-29 on 1m 37.649s, Sebastian Vettel on 1m 37.686s in the other RB10 and Daniil Kvyat for Toro Rosso on 1m 37.714s.
One of the main focal points of the 90-minute session was the official Grand Prix weekend debut of Max Verstappen. The 17-year-old Dutchman hardly put a wheel wrong and was 12th fastest on 1m 38.157s in the second Toro Rosso, and given his inexperience of both car and track the 0.443s gap to Kvyat was very respectable. His running came to an early end however when he suffered an apparent engine failure seven minutes from the finish, forcing him to pull off circuit at Turn 6.
Felipe Massa was 11th for Williams with 1m 38.012s, while behind Verstappen the Force Indias of Sergio Perez and Nico Hulkenberg recorded laps of 1m 38.324s and 1m 38.582s respectively; the German having a couple of minor offs.
Romain Grosjean took his Lotus to the 15thfastest time of 1m 38.851s, ahead of Adrian Sutil's Sauber on 1m 39.046s, Pastor Maldonado's Lotus on 1m 39.097s and Esteban Gutierrez's Sauber on 1m 39.318s.
Marcus Ericsson lapped his Caterham in 1m 40.031s to claim 19th ahead of team mate Roberto Merhi, the Spaniard driving Kamui Kobayashi's CT05 in FP1. Merhi had an early spin at Spoon Curve, but was otherwise assured en route to a 1m 41.472s - enough to edge the Marussias of Jules Bianchi and Max Chilton, on 1m 41.580s and 1m 41.757s respectively.