The 29-year-old German clocked a best lap of one minute and 36.067 seconds in the final moments to outpace his nearest rival, Mercedes team-mate and championship leader Hamilton by almost four-tenths of a second.
Until qualifying, Hamilton had reeled off fastest laps in all three practice sessions and demonstrated the speed and form that suggested he was in line for his fifth straight win and 10th this year in Sunday's 56-lap race.
"Great job guys," said Rosberg. "Thank you very much."
It was his 13th career pole and meant he had out-qualified Hamilton 10-7 over the season so far.
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"A great day, very happy," he added.
"It worked out really well. Together with my engineers, I arrived in qualifying with a car that I was really happy with for qualifying.
- Hamilton's braking problems -
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Hamilton revealed that he has endured braking problems throughout the weekend.
"Nico did a great job," he said. "I was struggling with braking. The left brake was always about 100 degrees less than the right and kept catching, no matter what I did.
"Even if I braked earlier, it was still locking. Perhaps that's where I lost a lot of the time. Even if that was the case, Nico was quicker today. Potentially, it's a problem for the race so we need to see if they can scrub them down.