Rosberg led all 78 laps around the Principality and was comfortably ahead of runner up Sebastian Vettel.
Vettel and team-mate Mark Webber overtook Lewis Hamilton during a safety car period to clear up debris following an accident for Felipe Massa.
Massa suffered a carbon copy of his practice shunt and was taken to the medical centre as a precaution.
Racing resumed but the action was red flagged on Lap 46 after a crash between Pastor Maldonado and Max Chilton.
Chilton moved over on Maldonado, launching the Williams into the barriers at Tabac. The Tech-pro barrier subsequently broke and the race was halted so repairs could be carried out.
While the top four eased ahead, the battle for fifth place was frantic.
Sergio Perez had already overtaken Jenson Button and Fernando Alonso but ran out of luck when attempting a move on Kimi Raikkonen.
Perez was forced into the barriers and later retired. Raikkonen stopped for repairs but still came home in tenth.
That contact left Adrian Sutil in a fine fifth place. The German had pulled off a couple of sublime moves at the hairpin on Button and Alonso to record his best finish of the season.
Button was sixth, while Alonso came home in seventh.
Jean-Eric Vergne equalled his best result with a stellar drive to eighth, ahead of Paul di Resta and Raikkonen.
The safety car was also deployed for a late crash between Romain Grosjean and Daniel Ricciardo.