Hamilton crashed in qualifying to end up so far back on the grid and added a front wing injury to his woes after a mishap while passing fellow Briton Jenson Button at around the halfway mark.
Valtteri Bottas would have felt more than Hamilton’s breath down his next as the race came to its closing stages but didn’t let him pass.
In a rare moment for the season Aussie Daniel Ricciardo was beaten by teammate Sebastian Vettel as the four-time world champion managed fourth ahead of his younger mate’s sixth.
Rosberg is now 14 points ahead of Hamilton in a Mercedes one-two for the championship.
“I had great fun,” said Hamilton. “I did as good as I could today. It was very hard to get through the field safely.
“I had a little collision with Jenson. I really thought he was opening the door for me; he has been very good like that in recent races. So my bad on judgement there.”
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