The 2008 Formula One world champion easily pulled away from his rivals on a dry track with a three-stop strategy to win the race by 17.
3 seconds, his 23rd career victory and first in Malaysia at the eighth attempt.
“Really grateful, thank you so much,” the Briton told his team over the radio after taking the chequered flag for his second win for Mercedes since he joined them last year and first points of the season.
Rosberg, who won the season opener in Australia two weeks ago, started in third place but slipped past quadruple world champion Sebastian Vettel on the first corner and was able to keep the Red Bull at bay and stay top of the driver standings.
Vettel finished third, 7.2 seconds behind Rosberg, for his first points of the season following an early retirement in Australia as he struggled to make an impact on the Mercedes pair without the rain that helped his qualifying bid on Saturday.
Ferrari’s Fernando Alonso secured his second fourth finish of the season after coming out ahead in a tight battle with Force India’s Nico Hulkenberg in the closing stages.
McLaren’s Jenson Button was sixth with Felipe Massa of Williams seventh just ahead of team mate Valtteri Bottas after the Brazilian refused to yield to his Finnish team mate despite team orders to do so.
McLaren’s Danish rookie Kevin Magnussen and Toro Rosso’s Russian newcomer Daniil Kvyat rounded out the top 10 of a race that suffered just a couple of light drops of rain despite concerns about possible thunderstorms.
Red Bull’s Daniel Ricciardo, who was disqualified in Australia pending an appeal, missed out on points for the second race in a row after a disastrous third pit stop when he was in fourth.
The Australian pulled away before his front left wheel was fully attached with engineers sprinting down the pitlane to push him back and fix the issue.
The Australian was then given a 10 second penalty for the unsafe release but his chances of points were already over after he shredded a tyre and damaged a wing shortly before the stewards’ decision and he retired before the end.
(Reporting by Patrick Johnston, editing by Alan Baldwin)