The 29-year-old German trailed championship-leading Mercedes team-mate defending champion Lewis Hamilton for 63 laps until an accident prompted a Safety Car intervention that, in turn, led the team to call the Briton in for an unexpected and unnecessary pit-stop.
Obeying his team, Hamilton, who led by 21 seconds before he pitted, came out in third place and, after the race was re-started with eight laps remaining, found it impossible to pass Sebastian Vettel's Ferrari, let alone Rosberg, to claim his fourth victory of the year.
Rosberg's triumph enabled him to join Briton Graham Hill, Frenchman Alain Prost and Brazilian Ayrton Senna in completing a Monaco hat-trick. It was also his second win in a row, following his victory in Spain, and rekindled his challenge for the drivers' championship.
Until the Safety Car, after Dutch teenager Max Verstappen in his Toro Rosso had crashed at Ste Devote, it had been Hamilton's race, but he ended up settling for a disappointed third ahead of the two Red Bulls of Russian Daniil Kvyat and Australian Daniel Ricciardo.
Brazilian Felipe Nasr came home ninth for Sauber and remarkably, after starting from the pit lane, Spaniard Carlos Sainz finished 10th to score a point in the second Toro Rosso car.
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