Rosberg led from lights to flag to take victory around the streets of the principality, surviving two safety-car periods and a red-flag incident that forced a 25-minute delay. It was also the second victory of his Formula One career, both of them coming with Mercedes.
The 27-year-old becomes the first son of a former Monaco GP winner to finish on the top step of the podium of F1's blue-riband event.
But there was no Mercedes one-two as Lewis Hamilton lost out in the first safety-car spell, finishing fourth behind Red Bull's Sebastian Vettel and Mark Webber.
The first 30 laps gave little clue as to what was to happen over the final 48 as in true Monaco fashion, a procession ensued
From the start Rosberg and Hamilton maintained their one-two off the line, keeping the Red Bulls of Vettel and Webber at bay.
Up until that point there had only been three incidents of note, with the first a lap-one collision between Williams' Pastor Maldonado and Caterham's Giedo van der Garde, the latter losing his front wing.
Seven laps later, a bad day for Caterham was completed when Charles Pic's car caught fire, forcing the Frenchman into a hasty retreat as marshals doused the flames at Rascasse.
And not for the first time this season, McLaren team-mates Jenson Button and Sergio Perez found themselves at odds with one another.
With Perez twice cutting a corner as Button pressed from behind, the team ordered the Mexican to cede his seventh place at that time.
What followed from lap eight was the usual case of follow-my-leader, with the odd pit stop thrown in once the window began to open.
Then on lap 30 Felipe Massa sparked the activity that followed, in an accident which was a mirror-image of his smash yesterday during final practice.
The Brazilian sustained a sore neck after braking on a bump towards the end of the start-finish straight, his car instantly bottoming.
As he hit the brakes, Massa first smacked into a metal barrier to his left before sliding 100 metres and ploughing nose-first into one of F1's safety TechPro barriers at Ste Devote.
The repeat in the race brought out the safety car for the first time this year, and it remained on track for eight laps as the medical car waited in attendance while Massa had a neck brace fitted.
It prompted a flurry of stops for tyres, with Hamilton the loser as he and Rosberg were the last to pit given their positioning on the circuit at the time of Massa's crash.
In double stacking in the pits, although Rosberg managed to retain his lead, Hamilton dropped to fourth behind Vettel and Webber, with Mercedes motorsport director Toto Wolff suggesting he was slow in.
The race resumed on lap 38, but eight laps later it had to be red-flagged when Maldonado and Marussia's Max Chilton collided on the approach into Tabac.
Maldonado was sent momentarily airborne before hurtling nose-first into another set of TechPro barriers at the Tabac corner, the impact forcing them to concertina on to the circuit itself.
With the situation too dangerous to run behind the safety car whilst repairs were carried out and debris cleared, race director Charlie Whiting had no alternative but to temporarily halt the race.
With the cars lining back up on the grid, and all able to switch to new rubber, it was 25 minutes before the racing resumed.
Then on lap 63 the safety car came into play for a second time when Romain Grosjean in his Lotus ran into the back of Toro Rosso's Daniel Ricciardo coming out of the tunnel.
With carbon fibre debris strewn across the circuit, it again led to a bunching of the field behind the safety car for three laps.
Through it all Rosberg kept his composure, and whilst other incidents unfolded behind him.
Notably, Perez, who had pulled off brave moves on Button and Alonso into the chicane, went one too far on Raikkonen as he was squeezed into a barrier which led to front-wing damage.
Although he attempted to continue, he eventually retired three laps from home, and to the likelihood of facing another talking to from team principal Martin Whitmarsh.
Raikkonen sustained a left-rear puncture, but despite a late stop he still rescued 10th to extend his remarkable run in the points to 23 races, one behind Michael Schumacher's all-time record.
But it means the Finn is now 21 points behind Vettel, with Alonso a further eight back after he could only finish seventh behind Force India's Adrian Sutil in fifth and Jenson Button in his McLaren.
Behind Alonso, Jean-Eric Vergne was eighth for Toro Rosso, with Paul Di Resta ninth in his Force India after starting 17th.
Monaco Grand Prix Final Standings
1. Nico Rosberg (Mercedes) - 17:52.1
2. Sebastian Vettel (Red Bull) - +3.8s
3. Mark Webber (Red Bull) - +6.3s
4. Lewis Hamilton (Mercedes) - +13.8s
5. Adrian Sutil (Force India) - +21.4s
6. Jenson Button (McLaren) - +23.1s
7. Fernando Alonso (Ferrari) - +26.7s
8. Jean-Eric Vergne (Toro Rosso) - +27.2s
9. Paul di Resta (Force India) - +27.6s
10. Kimi Raikkonen (Lotus) - +36.5s
11. Nico Hulkenberg (Sauber) - +42.5s
12. Valtteri Bottas (Williams) - +42.6s
13. Esteban Gutierrez (Sauber) - +43.2s
14. Max Chilton (Marussia) - +49.8
15. Giedo van der Garde (Caterham) - +62.5s
Sergio Perez (McLaren) - Retired on Lap 72
Romain Grosjean (Lotus) – Retired on Lap 63
Daniel Ricciardo (Toro Rosso) – Retired on Lap 61
Jules Bianchi (Marussia) – Retired on Lap 58
Pastor Maldonado (Williams) – Retired on Lap 34 laps
Felipe Massa (Ferrari) – Retired on Lap 28
Charles Pic (Caterham) – Retired on Lap 8