German Rosberg, 29, clocked an early best lap of one minute and 35.424 seconds to take the initiative ahead of Hamilton, who wound up seven-tenths of a second slower than his team-mate on a windy morning. (Agencies)
Rosberg leads Briton Hamilton, 29, the 2008 world champion, by 29 points in this year's title race after eight closely-contested races.
Two-time champion Spaniard Fernando Alonso of Ferrari was third ahead of Australian Daniel Ricciardo of Red Bull, Finn Kimi Raikkonen, the 2007 champion, in the second Ferrari and defending four-time champion German Sebastian Vettel in the second Red Bull.
Briton Jenson Button, the 2009 champion, was seventh for McLaren ahead of the two Red Bulls of Russian rookie Daniil Kvyat and Frenchman Jean-Eric Vergne with Danish rookie Kevin Magnussen, 21, making up the top ten in the second McLaren.
Meanwhile Susie Wolff's bid to make a mark as the first woman to take part in a Grand Prix weekend for 22 years ended prematurely when her Williams car suffered an engine failure.
The 31-year-old Scot clocked only three laps in the opening minutes, producing a best time of one minute and 44.212 seconds before she pulled off and parked the car after an oil pressure warning.
Within a few minutes, her Williams team-mate Brazilian Felipe Massa joined her on the sidelines after a spectacular accident that saw him rip the front left wheel off his car and damage the gearbox.
Massa was unhurt, but both cars were ruled out of action for the rest of the session.
Wolff returned to the pits - after her brief outing that ran for less than 20 minutes - to speak to her race engineer who told her: "The engine has gone... It's terminal."
Her disappointment was evident as she turned away.
She later told reporters that, though she was disappointed, it was the way of things in Formula One.
"I am so grateful to everyone for the support I have had here this weekend and now, at least, I have been out and got the first start out of the way.
"I can at least look forward to having another run at Hockenheim."
German Rosberg, 29, clocked an early best lap of one minute and 35.424 seconds to take the initiative ahead of Hamilton, who wound up seven-tenths of a second slower than his team-mate on a windy morning.