Hamilton was on pole but a poor start saw him drop to sixth as Rosberg, Ferrari's Sebastian Vettel and Kimi Raikkonen, Valtteri Bottas in Williams and Red Bull's Daniel Ricciardo all flew past him on Sunday.
Rosberg finished the race in one hour 17 minutes 28.089 seconds, 15 seconds clear of the three-time defending champion, reports Xinhua.
Hamilton now leads the title race with 250 points ahead of Rosberg on 248.
Sebastian Vettel came third, 5.9 seconds further adrift, ahead of his Ferrari team-mate Kimi Raikkonen to the delight of the home fans.
Daniel Ricciardo finished fifth for Red Bull ahead of Valtteri Bottas of Williams.
