While Rosberg was dominant in his fully functioning W05, his pole-sitting team-mate Lewis Hamilton lasted only four laps before a misfiring cylinder ended his race.
World champion Sebastian Vettel was also an early retiree after power problems in his Red Bull, underlining this year's unpredictability as teams grapple with new hybrid technology.
"Despite our success, we also know that there is still some work to do," said Rosberg, who streaked away from third on the grid for a wire-to-wire victory.
"We have two weeks to improve that. I am very much looking forward to (the next race in) Malaysia and I would love to race again tomorrow."
Red Bull's Daniel Ricciardo was disqualified from second place for violating fuel rules, in another illustration of the challenges facing teams this year.
But McLaren were rewarded for getting both their cars to the finish line, with debutant Kevin Magnussen classified second and Jenson Button third after Ricciardo's disqualification.
"We know that reliability will be crucial to this long season and we will be working hard to improve the situation for the race in Malaysia," said Mercedes team boss Toto Wolff.
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