The Mercedes driver benefitted from the problems that hit team-mate Lewis Hamilton and Red Bull's Sebastian Vettel - who both retired from the lead - to clinch his second victory in three races, having also won in Monaco.
The result left Rosberg 50 points behind Vettel in the standings.
Rosberg was delighted with the progress Mercedes has made with its tyre management issues, but reckons it is too early to get carried away.
"I wouldn't talk about that yet," said Rosberg when asked about his championship hopes.
"The team has already done such a fantastic job over the winter to come up with such a quick car in qualifying, and now we're progressing with tyre management too and it's giving us a car quick enough to win races."
Rosberg felt Mercedes had a car that was at least as quick as Red Bull, and admitted the victory had been very special for him.
"It feels fantastic, it's a very, very special day. What makes it most special is that our factory is so close," he said.
"The team has done such a fantastic job. We have such momentum at the moment.
"We're making progress all the time. We're massively quick in qualifying and we're getting faster and faster in the race. I think today we had the equal fastest race car as well."
The German said he felt sad for team-mate Hamilton, who suffered a tyre blow-out while leading from pole.
"With Lewis I definitely feel sorry for all the British fans as it would've been a great race for Lewis in front of his home crowd."
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