Following up Germany's World Cup triumph in Brazil last weekend, his wedding in Monaco and the signing of a new contract with Mercedes, Rosberg led untroubled from pole position to chequered flag.
Lewis Hamilton, his team-mate and only real title rival, finished a fighting third after starting in 20th place and then charging through the field.
Finland's Valtteri Bottas took second place for Williams - his third podium finish in a row - a hefty 20.7 seconds behind Rosberg, after his Brazilian team-mate Felipe Massa crashed at the start to bring out the safety car.
Rosberg was the first to win for a works Mercedes team in Germany since the Argentine Juan Manuel Fangio in 1954 and first German winner for a German team since the championship started in 1950. "It's fantastic. It's an amazing feeling to win here at home," he said. "A special day for me."
Rosberg is now sitting on 190 points to Hamilton's 176 with Australian Daniel Ricciardo 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 so far in 2014 and in normal circumstances would have been celebrating another one-two finish on an overcast afternoon that only turned to rain after the finish.
The 50,000 spectators, a disappointing attendance in a season dominated by Mercedes, 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.
Mercedes had warned the fans to buckle up for the ride and Hamilton delivered with a swashbuckling drive that saw him go three abreast at times, picking off a Ferrari and a 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.
Hamilton said he thought Button was allowing him to pass. "Why would we let anyone through?" asked a bemused Button. "I don't know if you've noticed, but a lot of drivers do that line to get a good exit from the corner. It's strange, but when the car's so much quicker you'd think he wouldn't get into so many fights, but there you go."
Hamilton could not get past Bottas - the Finn became the first Williams driver since Colombian Juan Pablo Montoya in 2003 to rack up three successive podiums - but enjoyed his day anyway. "I had great fun," said Hamilton on the podium. "I did as good as I could. It was hard to get through the pack safely and I had a little bit of a collision with Jenson. I thought he was going to open the door which he has done a couple of times lately but that was my bad judgement. It was hard to overtake so I'm glad to get some points today."
Germany's quadruple champion Sebastian Vettel, last year's winner at the Nuerburgring, was fourth for Red Bull ahead of Ferrari's Fernando Alonso in fifth. Ricciardo was sixth for Red Bull ahead of Force India's Nico Hulkenberg and Button. Danish rookie Kevin Magnussen, who tangled with Massa at the start when they lined up third and fourth, recovered to take ninth place while Mexican Sergio Perez made it a double scoring finish for Force India.