Rosberg's win was the first for a works Mercedes team in Germany since Argentine Juan Manuel Fangio in 1954, and his fourth victory of the season.
Lewis Hamilton, his team-mate and only real title rival, finished third after starting in 20th place and then charging through the field on an overcast afternoon that threatened rain without delivering.
Finland's Valtteri Bottas took second place for Williams, his third podium finish in a row, after Brazilian team-mate Felipe Massa crashed at the first corner in a collision with Kevin Magnussen that brought out the safety car.
Sebastian Vettel led the chasing pack, taking fourth ahead of Fernando Alonso, Daniel Ricciardo and Nico Hulkenberg; and Jenson Button finished in eighth after a late pit stop which led him to muse over the radio to his team that the strategy had been wrong.
There was a dramatic moment on lap 44 as Danii Kvyat's Toro Rosso burst into flame. Fortunately the driver managed to manoeuvre the car off the track and then free himself from the cockpit.
Adrian Sutil also suffered a mechanical problem in his Sauber, spinning and then stalling on the straight, forcing another and rather lengthy yellow flag on lap 47 until the car was removed from the track.
After the race, Jean-Eric Vergne was given a five-second penalty for exceeding track limits during his battle with Romain Grosjean in the German Grand Prix.
The Toro Rosso Formula 1 driver, who had already been given a five-second stop-and-go for exceeding track limits during the race, was also awarded a penalty point for the incident.
Race stewards deemed Vergne had gained an advantage by going off the track while fighting with Lotus driver Grosjean at Turn 6.
The time penalty does not affect Vergne's position, however, with the Frenchman still classified 13th. He had a gap of 6.3s back to 14th-placed Esteban Gutierrez before the extra sanction.
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