Rosberg - the winner on F1’s last visit to Hockenheim in 2014 - lapped nearly four tenths quicker than Hamilton, but in contrast to the morning session both Ferraris and both Red Bulls were also able to get within a second of the German on the supersoft tyres.
Another home favourite, Sebastian Vettel, was the quickest of them, seeing off the closely matched RB12s of Max Verstappen and Daniel Ricciardo and team mate Kimi Raikkonen's identical SF16-H.
Hamilton had earlier set the pace on the soft tyre, but the world champion’s supersoft lap was a bit scrappy, with a big lock-up going into the hairpin, and he couldn’t get on terms with Rosberg.
This time it was Force India who got closest to the top three teams courtesy of Nico Hulkenberg who lapped his VJM09 in 1m 16.781s to head McLaren’s Jenson Button, team mate Sergio Perez and birthday boy Fernando Alonso, whose efforts to improve on 10th fastest led to a prolonged slide on the kerb exiting Turn 3.
McLaren's session ended in unusual circumstances however as Button headed to the medical centre shortly before time expired after reporting an eye issue. He later headed to hospital for further checks.
Times, as ever, were very close in the midfield, with just a second separating Button in eighth and Renault’s Kevin Magnussen in 17th.
Tyre wear will be a factor here, as the long runs demonstrated. Vettel, for example, told his team “I’m wasting my time here. What do you want me to do?” Asked whether he wanted the front wing flap adjusted, he snapped back that he was doing it all by himself as his crew had not apparently noticed he was running in traffic the whole time.
Hamilton also had stern words over team radio after a close moment when Ricciardo passed Rio Haryanto’s just as the Mercedes man exited the pits. There was a similarly tight moment at Turn 8 too as Raikkonen ran Felipe Massa’s Williams wide at Turn 8 after a passing attempt in the hairpin had been rebuffed.
The other big talking point throughout the session was drivers running wide at Turn 1 - behaviour that race director Charlie Whiting had earlier warned would see drivers reported to the stewards.
Vettel, Verstappen and Perez were amongst those who were adjudged to have gone off track and continued multiple times at the corner.
