Mercedes-powered Williams filled the second row with Finland’s Valtteri Bottas third fastest and Brazilian Felipe Massa fourth.
Hamilton leads Rosberg by 17 points with three races, and 100 points remaining. The Briton has won the last four grand prix and is chasing his 10th victory of the season.
If the pair finish one-two on Sunday, as looks more than likely, Mercedes will equal McLaren’s record of 10 in a season set with Alain Prost and the late Ayrton Senna.
The pole was the ninth of the season for Rosberg and 13th of his career.
“It worked out really well. Together with my engineers, I really arrived in qualifying with a car that I was really happy with,” said Rosberg.
“This morning, the conditions were quite different, a lot colder so the track was changing all the time. It wasn’t that easy to get everything right.
“First place today is awesome, but the race is what counts, so I need to fully focus on tomorrow and try and bring it home,” added the German
Hamilton, who had been quickest in all three practice sessions and the first phase of qualifying, had tyre and brake issues when it mattered most and expressed some concern for Sunday.
That race comes on the sixth anniversary of his 2008 world championship triumph in Brazil.
“The issue was just locking and if I can’t fix that brake then that will be a continuing issue throughout the race,” said Hamilton.
Australian Daniel Ricciardo qualified fifth for Red Bull while his team mate and 2013 winner Sebastian Vettel starts from the pitlane after exceeding his engine allocation for the season.
Ferrari’s Fernando Alonso qualified sixth.
There was also a ray of hope for beleaguered Sauber, who have yet to score a point this year, with Germany’s Adrian Sutil qualifying 10th.
(Reporting by Alan Baldwin. Editing by Steve Keating.)