Rosberg's time of 1:32.330 was over two tenths of a second quicker than compatriot Sebastian Vettel.
Ferrari's Fernando Alonso will start from third place, alongside team-mate Felipe Massa.
Massa set only the sixth fastest time but has been elevated courtesy of penalties to Lewis Hamilton and Mark Webber.
Force India share the third row of the grid, with Paul di Resta ahead of Adrian Sutil.
Webber will start from seventh, with Kimi Raikkonen in eighth place.
Hamilton's penalty drops him to ninth, alongside former team-mate Jenson Button, who opted not to set a time in order to give himself a choice of tyres for the start of the race.
Late Q2 improvements bumped Lotus's Romain Grosjean out of the top 10. The Frenchman made a mistake on his first run and he will start from eleventh place.
Sergio Perez again failed to progress to Q3 and lines up twelfth, ahead of Daniel Ricciardo and Nico Hulkenberg.
The Williams drivers set identical lap times in Q1, but Valtteri Bottas set his time first and he progressed to Q2, where he finished in fifteenth place. Pastor Maldonado was knocked out in the first session and lines up in seventeenth.
Esteban Gutierrez again fell at the first hurdle. His eighteenth place becomes twenty-second once his grid penalty is applied.
For the first time this season, Caterham outqualified Marussia, with Charles Pic leading Jules Bianchi.