Untroubled from pole position to chequered flag, the newly-married German’s commanding victory added another highlight to a week that had begun with the signing of a multi-year contract extension.
Lewis Hamilton, his team-mate and only real title rival, finished third after starting in 20th and then making 15 overtaking manoeuvres as he charged back through the field in one of the more determined drives of his career.
Finland’s Valtteri Bottas took second for Williams, his third podium finish in a row, 20.7 seconds behind Rosberg, after Brazilian team-mate Felipe Massa crashed at the start in a spectacular collision.
Rosberg was the first to win for a works Mercedes team in Germany since Argentine Juan Manuel Fangio in 1954 and first German home winner for a German team since the championship started in 1950.
“What a great day after so many great events for me this week,” he said. “I came here hoping for a win and it worked out perfectly.”
“That was the best feeling,” he said of his Monaco wedding last week. “But of course everything has been special... many positive things happening in the two weeks, or week and a half. It’s been really enjoyable, and also this weekend with pole and the win. Just awesome. A very, very special day today.”
Rosberg now has 190 points to Hamilton’s 176 with Australian Daniel Ricciardo third on 106.
The German’s fourth victory of the season had looked inevitable from the moment a brake disc failed on Hamilton’s car in the first phase of qualifying on Saturday, sending the Briton spinning hard into the barriers.
Between them, the Mercedes drivers have won nine out of 10 races in 2014 and in normal circumstances would have been celebrating another one-two on an overcast afternoon that only turned to rain after the finish.
The 50,000 spectators were treated instead to the sight of Hamilton on a charge to limit the damage and a series of other thrilling duels further down the field.
Hamilton delivered with a swashbuckling drive that saw him go three abreast at times, picking off Kimi Raikkonen’s Ferrari and Ricciardo’s Red Bull in one swoop.
Hamilton was 10th after 10 of the 67 laps and up to second after 16, banging wheels and bodywork along the way but escaping with only a damaged front wing when he clipped former team mate Jenson Button’s McLaren.
Had he not damaged the wing and lost downforce, he would probably have passed Bottas. But he could not prevent the Finn becoming the first Williams driver since Colombian Juan Pablo Montoya in 2003 to rack up three successive podiums.
Germany’s quadruple champion Sebastian Vettel was fourth for Red Bull ahead of Ferrari’s Fernando Alonso in fifth.