The Mercedes driver - who has got married, signed a new contract and watched his German compatriots win the football World Cup in the past seven days - clocked a best time of one minute, 19.131 seconds in the first session at his home grand prix on Friday.
Team-mate Lewis Hamilton (+0.065secs), winner at Silverstone a fortnight ago, was second while Ferrari's Fernando Alonso (+0.292secs) came third.
There was good news for Williams development driver Susie Wolff, too, as she recorded the 15th quickest time to put the disappointment of the British Grand Prix behind her.
Wolff completed just four laps there and things looked bleak when she appeared to lose power again on the Hockenheim circuit on Friday, but a pit stop resolved the issue and she ended up just 0.227secs behind team-mate Felipe Massa.
An FIA ruling ensured that no team could utilise the front and rear interconnected suspension system, with the governing body arguing that it had become an aerodynamic aid.
It had been thought that the rule change would impact on Mercedes more severely than any other constructor, but that proved unfounded as Rosberg and Hamilton again left the field behind.
Defending champion Sebastian Vettel, who has endured a frustrating campaign so far, ranked sixth in his Red Bull.