The 28-year-old German came home 9.2 seconds clear of nearest rival and team-mate Lewis Hamilton who coped with loss of vision in one eye as he held off Australian Daniel Ricciardo's Red Bull in the closing laps.
It was Rosberg's second consecutive victory in his home event, his second win of the 2014 season and the fifth win of his career.
Fernando Alonso finished fourth for Ferrari ahead of Nico Hulkenberg of Force India and Jenson Button who finished sixth for McLaren.
Felipe Massa came home seventh for Williams, Jules Bianchi was eighth for Marussia ahead of fellow-Frenchman Romain Grosjean of Lotus and Kevin Magnussen finished 10th in the second McLaren.
Rosberg's win carried him to 122 points in the title race ahead of Hamilton, who was only half a second ahead of Ricciardo as they crossed the line, on 118.
"It's another special day for me, for sure," said Rosberg. "Lewis drove well and pushed me massively hard. The pressure was on but I kept it cool and pulled a bit of a gap at the end because of the refreshed tyres. Thanks to the team for all their great work."
On an overcast afternoon in the Mediterranean principality, with an air temperature of 20 degrees Celsius and a track temperature of 28, there was palpable tension in the air before the start.
Following Saturday's controversy, after Rosberg had gone down an escape road on his final lap, and Hamilton's threat to 'take a leaf out of Senna's book', fireworks were expected.
Hamilton did not in public at any rate congratulate Rosberg or make any contact with his teammate on the podium.
Given the drama of 24 hours earlier Hamilton and his Mercedes team-mate delivered a damp squib when the lights went out, Hamilton following Rosberg down to Ste Devote.
As the two Mercedes streaked clear, separated by less than a car's length on the opening lap, Raikkonen made the most of a fast start in his Ferrari to take fourth place behind Sebastian Vettel, who had jumped team-mate Ricciardo off the grid.
Vettel's good start counted for little, however, as he was soon hit by a loss of power and gearbox problems. "Come on guys," he said, on the team radio. "I'm sure you are trying everything..." And then "I'm stuck in first gear."
He retired on lap eight, joining the luckless Latin Americans Venezuelan Pastor Maldonado, whose Renault did not start, and Mexican Sergio Perez, who was hit by Briton Jenson Button's McLaren at the Mirabeau corner on the opening lap, on the sidelines. The safety car came out for the first time.
Soon after, on lap 25, Adrian Sutil, who had been charging hard, finally lost control at the chicane and hit the barriers, triggering a second safety car intervention which, in turn, caused the leaders to dive into the pits for fresh tyres on laps 27 and 28 respectively.
Racing resumed on lap 30 when Raikkonen had dropped to 14th after a collision and puncture and Vergne's Toro Rosso crew released their driver directly - and dangerously into the path of Kevin Magnussen's McLaren.
Vergne, running sixth, was given a drive-through penalty that dropped him to 12th before an engine failure later ended his race.
Hamilton remained virtually glued to Rosberg's tail, just six-tenths of a second behind, as they led the field by more than seven seconds. Hamilton clearly believed incessant pressure might force an error as the race unfolded.
At half-distance, Rosberg was warned that he needed to use higher gears to conserve fuel for the closing laps when Hamilton was expected to attack again.
This seemed certain until, with 14 laps to go, Hamilton's vision was impaired, causing him to ease off by four seconds.
"I can't see out of my left eye - I've got some dirt, or something, in my eye," he reported.