Rosberg crossed the line first on a dramatic afternoon at Silverstone, capitalising on a mechanical failure on Sebastian Vettel's Red Bull in a race marred by four identical Pirelli tyre failures.
But the FIA had asked Rosberg and a team representative to report to the race stewards, with 1992 world champion Nigel Mansell among their number, for appearing to fail to observe the yellow flags.
However, he was reprimanded, rather than handed a time penalty, rubber-stamping his second win of the season and third of his career.
Rosberg committed the offence between turns three and five at 14.06pm and, while the stewards found he had not made the required significant reduction in speed required, a reprimand was deemed sufficient punishment.
Once Vettel retired with a gearbox problem at the end of lap 41, Rosberg held off Mark Webber's late charge to take the win by just 0.7 seconds.
Ferrari's Fernando Alonso took advantage of championship leader Vettel's troubles with third place, closing his deficit to the German to 21 points.
Pole sitter Lewis Hamilton was fourth, but was left bitterly frustrated having led the early laps before becoming the first driver to fall victim to a Pirelli tyre failure.
The win was particularly sweet for Mercedes, with the team's Brackley base being so close to Silverstone, and Rosberg dedicated his win to the team.
He said: "It has been a fantastic day. It is very special because it is the home grand prix of the team and the factory is 10 minutes away.
"A lot of people, a lot of my fellow team members and colleagues were in the grandstands and it's very, very nice that I was able to give them such a great race and such a great result.
"They really deserve it because they've worked so well all season.
"It's great to see the momentum we have in the team at the moment."
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