The pole sitter, cheered on by Germany World Cup winner Lukas Podolski in the Mercedes pits, extended his lead to 14 points over teammate Lewis Hamilton, who charged up to finish third from 20th on the grid.
"It's an amazing feeling to win at home. It's a very special day," said Rosberg.
Splitting the Mercedes men in second was the Williams of Valtteri Bottas.
Rosberg came home a comfortable 20.7 seconds ahead of the Finn at the end of an enthralling 67-laps contest.
Rosberg's win came after a week in which he had married his long-term girlfriend Vivian Sibold, signed an extended contract with Mercedes and celebrated Germany's World Cup victory.
It was his fourth win of the season and the seventh of his career.
But even such joyful supremacy was overshadowed in an incident-filled race by the bold passing pace of Hamilton, who started at the rear of the grid following his high speed crash in qualifying.
I had great fun," said Hamilton.
"I did as good as I could. It was hard to get through the pack safely... It was hard to overtake so I'm glad to get some points today.
