The Mercedes AMG Petronas driver salvaged a podium place after title rival and reigning world champion Lewis Hamilton retired.
Rosberg’s race looked over at the Sepang International Circuit following a first lap incident with Sebastian Vettel.
Hamilton, who started on pole, looked all over the winner before he was forced to retire on lap 41 after a sudden failure of his internal combustion engine, which occurred with no prior warning
Rosberg now leads the FIA Drivers’ Championship by 23 points from his Brackley team-mate.
Rosberg said: “I came here with the will to win and that didn’t work out, so I can’t say that I am happy.
“But after the first corner, it was looking pretty dark. I thought my race was over and never thought I’d be able to continue.
“I was fortunate to be able to fight through the field but I got the knife between my teeth and went for it. I fought my way through, with some great battles along the way which I really enjoyed, and was pleased to make it back up to the podium.
“I had to give it everything at the end to eke out that ten second gap but at the same time save the engine. You just never know what’s going to happen next.”
Hamilton said: “Max [Verstappen] was in my pit window so I was just trying to push him out of it.
“But then, on the straight, I just lost power all of a sudden. You could hear something blew and I obviously had to stop.
“When you get out of the car, that feeling you have after leading the race and then your car fails, it’s pretty hard to say positive things at the time.
“But it’s my fourth year with them now and the guys in the garage and back at the factories, I have 100 per cent faith in them.”
Team boss Toto Wolff said: “The task is to pick ourselves back up for Suzuka.
“One of the greatest qualities of our group is how we come back from defeat even stronger than before. We will do that again now, in time for Japan next weekend.
“For Nico, it was a great recovery drive after what happened. He was unlucky to be hit by Sebastian [Vettel] but fortunate the car did not sustain more damage.”