The German's Mercedes was jumped at the start by Daniel Ricciardo. But after avoiding the first-corner mayhem unfolding behind the front two, he quickly caught the Red Bull and romped home to win by a whopping 38 seconds from Ferrari's Sebastian Vettel.
Reigning world champion Lewis Hamilton began from the back of the Shanghai grid after a mechanical failure on his Mercedes sabotaged qualifying for the Briton on Saturday. But he roared back to take seventh, despite pitting early to replace a damaged front wing.
Ferrari's wretched fortunes continued after Vettel and Kimi Raikkonen collided at the first turn, allowing Daniil Kvyat's Red Bull to slip past into third, which is where the Russian finished.
Vettel carved his way back through the field from 15th but blamed Kvyat for driving "like a madman" in a furious rant over the team radio.
"Kvyat's attack was suicidal," fumed the German, who was still squabbling with Kvyat as Rosberg made his victory speech.
The four-time world champion admitted he was fortunate even to finish the race.
"I was very lucky to continue," said Vettel. "It was a big hit with Kimi. I feel very sorry for Kimi but I was a bit in a sandwich between Kimi and Daniil and there was nothing I could do.
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