Pole-sitter Rosberg slumped to fourth off the start-line, and his torrid afternoon took another twist when he was hit with a five-second penalty for an overzealous pass on Max Verstappen.

The German finished behind both Red Bull drivers, with Daniel Ricciardo and Max Verstappen completing the podium places.

Hamilton was left kicking himself on Saturday night after a mistake in qualifying paved the way for Rosberg to claim pole.

But the defending champion vowed to bounce back with a victory here in Hockenheim and he did not disappoint.

Just as in Hungary seven days ago, the Stevenage-born racer emphatically beat Rosberg off the line and from there his victory never looked in doubt.

In contrast, Rosberg will be desperate to forget a home race which turned sour from the moment the lights flicked to green.

The German, who was quickest in all three practice sessions before claiming pole, was fourth after his sluggish start, and he spent much of the opening phase of the race behind the Red Bull drivers with Verstappen initially running in second after a bold overtake around the outside of his team-mate at turn one.

With Rosberg adopting a different strategy to Ricciardo, he emerged from his second stop behind Verstappen, and on the run down to the hairpin on lap 29 he dived underneath the Dutchman.

But as in the controversial race in Austria earlier this month, in which he collided with Hamilton on the final lap, Rosberg appeared to leave little room for the Dutchman.

The 18-year-old was forced to take to the escape route, and following a brief investigation by the stewards, Rosberg was hit with a timed penalty.

The German protested his innocence. "Can you explain to them that I was full lock on the steering wheel," he said over the team radio.

But TV replays suggested it was an implausible defence. After serving his penalty at his third and final pit stop, Rosberg emerged with 22 laps remaining behind both Ricciardo and Verstappen, and that is how it remained.

Rosberg will now head into the three-week summer break having seen a 43-point championship lead over Hamilton turn into a 19-point deficit in just seven grands prix.

And with nine rounds remaining, Hamilton, whose early part of his season was fraught with car issues, will now be the overwhelming favourite to win his fourth title.

Sebastian Vettel and Kimi Raikkonen crossed the line in fifth and sixth for Ferrari while Jenson Button finished eighth for McLaren after passing the Williams over Valtteri Bottas on the penultimate lap.

British rookie Jolyon Palmer started 14th and made three places off the start-line, but a clumsy collision with Felipe Massa on the opening lap, saw him drop to last, and he ended the race only 19th.

Celebrating the 49th victory of his career, Hamilton said: "Today I didn't make any mistakes, so in my heart I am happy with what I did today. I came to do a job.

"Yesterday wasn't perfect but you learn from those things, and today was a real show of looking at the glass half-full."

Ricciardo added: "This is two weekends in a row on the podium and one of the most refreshing things is seeing all the fans back in Germany.

"A first double podium for Red Bull in over a year, so it's an awesome way to close out the first part of the season."