Rosberg, who was quickest on Friday, lapped the Silverstone circuit with a best lap of one minute 31.487 seconds on a bright and breezy day at the former World War two airfield that hosted the first championship race in 1950.
Hamilton, the 2008 champion and a home favourite, was 0.146 slower after Monaco winner Rosberg snatched the top place on the timesheets in the closing seconds.
Red Bull's triple world champion and championship leader Sebastian Vettel and Australian team maate Mark Webber were third and fourth fastest, but half a second slower than Rosberg, with Lotus's Romain Grosjean fifth.
Vettel leads Ferrari's Fernando Alonso by 36 points after sseven of 19 races.
McLaren's Jenson Button, the 2009 champion and another local favourite, was only 12th and Mexican team mate Sergio Perez was 18th after a left rear tyre blowout caused the session to be halted for marshals to pick up debris.
Perez also slid off later in a difficult session for his struggling team.
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