It was a slow-burner of a race, brought to life by the deployment of the safety car on two occasions, and even a red-flag incident.
Rosberg, top of the pile, found his tyres more forgiving than they have been elsewhere this season, and had more than enough to hold off Red Bull duo Sebastian Vettel and Mark Webber for second and third. Lewis Hamilton, undone by bad timing at his first pit stop, slipped to fourth place.
Controversy may yet overshadow the win - the build-up was dominated by news of a 'secret' test Mercedes ran after the Spanish Grand Prix together with Pirelli - the Silver Arrows' rivals have launched a protest at what could be perceived as an unfair advantage.
Adrian Sutil bagged fifth for Force India, Jenson Button grabbed sixth after a tangle between Kimi Raikkonen and Sergio Perez cost both drivers, ahead of Fernando Alonso.
Jean-Eric Vergne’s impressive weekend ended with eighth place, Paul di Resta put his qualifying woes to one side to claim ninth, while Raikkonen flew up the standings late on to nab the point which sealed a 23rd straight points finish for the Finn.
For Rosberg, it was a joyous day as he became part of the first father/son combination to win the Monaco, exactly 30 years after his father Keke had triumphed in a Williams.
But Vettel will be no less happy, having extended his advantage in the title race over his rivals – now 21 points clear of Raikkonen after six Grands Prix.
The drivers negotiated the first corner without major incident, and soon settled into a processional pattern. Sebastian Vettel swarmed over the back of Lewis Hamilton, but it was as close as anyone got to gaining or losing a place in the top six.
Mercedes backed up the field, lapping well within themselves and conserving their tyres for later in the race. Strategy became a game of cat-and-mouse, with drivers agonising over whether to pit early or be patient.
Passing was at a premium, with the only man to buck the trend di Resta, who beat Felipe Massa and Esteban Gutierrez around the outside at Ste Devote in exquisite moves.
But Massa crashed at turn one 30 laps in, a repeat of a shunt in practice, forcing the safety car out for the first time this year and shuffling the order.
The biggest loser was Hamilton; having had to ease off to allow a Mercedes double-stop, he found himself rejoining the race behind the two Red Bulls while Rosberg stayed out ahead.
Perez was the winner as the Grand Prix resumed – a brilliant opportunistic move at the Nouvelle Chicane getting him past Button, and a similar move on Alonso soon afterwards was only denied by the Spaniard cutting the chicane – the double world-champion was ordered to concede the place.
The race was red-flagged on lap 46 when Pastor Maldonado caught Max Chilton and flew into the barrier at Tabac. The barrier suffered more than the Venezuelan, but it meant a 20-minute delay, allowing an on-grid tyre change, before the race restarted.
When it did, Sutil pounced with two sharp moves against Button and Alonso at the Loews hairpin, but at the front there was no sign that Vettel could find a way past Rosberg.
A clash between the wild Romain Grosjean and Daniel Ricciardo put both out of the race and brought the safety car out once where it stayed until 11 laps remained.
Perez pushed his luck one time too many and broke his front wing in a battle with Raikkonen for fifth, with the Lotus suffering a puncture in the process. The Mexican lasted a few laps more, but his suspension eventually buckled under the strain.
It was, like every other incident, one that Rosberg had kept himself well away from, and he was a deserved winner of his second Grand Prix.