It was the Mercedes team's first victory in Britain since Stirling Moss won in 1955 and Rosberg's second in three races and third of his career and came just three days after he celebrated his 28th birthday.
But the race was overshadowed by a dangerous spate of Pirelli tyre failures, including one that blew home hero Briton Lewis Hamilton's hopes of a home win in the other Mercedes car as he led from pole position.
However, the 2008 world champion produced a remarkable drive to storm from last place - which is where he was when he resumed his race - to finish fourth.
Hamilton's tyre explosion was followed by others for Brazilian Felipe Massa of Ferrari, Frenchman Jean-Eric Vergne of Toro Rosso and Mexican Sergio Perez of McLaren in a contest that saw two Safety Car interventions.