Rosberg topped the session by 0.06s, but with Hamilton quicker in two of the three sectors it could be suggested that the Brit has more time in hand.
As has become customary, Fernando Alonso was third fastest for Ferrari, lapping three tenths shy of Rosberg. Next up were Daniel Ricciardo (Red Bull), Jenson Button (McLaren) and Sebastian Vettel (Red Bull).
Meanwhile teams were running without the front-rear interconnected suspension (FRIC) system for the first time. Early appearances suggest Williams may have lost pace as a result, with Felipe Massa their top performer in 11th. Susie Wolff, getting her first proper outing in an F1 session following technical gremlins at Silverstone, was 15th fastest.
Second practice gets underway at 14.00 local time at the Hockenheim circuit.