The German was a mere 0.070 faster than the double Formula One world champion in a troubled morning session but comfortably quicker in the afternoon when Hamilton was fourth and behind the Ferraris.
Rosberg, 10 points behind double world champion Hamilton after eight of the season's 19 races, lapped with a best time of one minute 34.274 seconds on a bright and hot morning at Silverstone and 1:34.155 in the afternoon.
Winner of three of the last four races, Rosberg had sat out much of the first session as mechanics changed his car's gearbox due to a hydraulic fault that stopped him on track with just five laps done.
Mercedes were reprimanded for covering up the car, against the rules, when it was returned to the paddock.
He had time for only 12 laps once the car had been fixed, compared to Hamilton's 26, but made up for lost time by getting quickly up to speed.
Hamilton, who can expect to have huge support from an expected 140,000-strong crowd on Sunday, had an early spin at Stowe without consequence but struggled with the setup after lunch.
"The car is all over the place. I can't go any faster than I am right now," he said over the radio. Rosberg was, meanwhile, told to cool the car.
Ferrari's Kimi Raikkonen, who crashed heavily in the previous race in Austria, was fourth and second while team mate Sebastian Vettel celebrated his 28th birthday with sixth and third respectively.
Germany's Nico Hulkenberg, with the updated Force India getting its first proper run, was ninth and eighth fastest behind the improving Red Bulls of Daniel Ricciardo and Daniil Kvyat, who were sixth and fifth in the second session.
Honda-powered McLaren's miserable run of form continued with Fernando Alonso and Jenson Button faster only than the Manor Marussias in the morning.
At one point in the afternoon, asked if he wanted to do another lap, Button replied: "No. The stability is terrible...the car's bouncing all over the place."
Three cars went off at Luffield in the afternoon, including Alonso, with Lotus's Romain Grosjean and Manor's Roberto Merhi briefly bringing out red flags when they got stuck in the gravel.
Development driver Susie Wolff made her sole appearance of the weekend for Williams in the morning and was 13th fastest.
(Editing by Ed Osmond)
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