Rosberg's third victory in a row, and 22nd of his career, lifted Rosberg on to 273 points, eight clear of Hamilton, with six rounds remaining.
Germany's Nico Rosberg celebrated his 200th Formula One race by retaking the championship lead from Mercedes team mate Lewis Hamilton after a pole to flag win in Singapore on Sunday.
After a chaotic start that brought out a safety car on the opening lap, Rosberg stayed clear of Red Bull's late charging Australian Daniel Ricciardo at the floodlit Marina Bay Street Circuit.
Triple world champion Hamilton completed the podium in third place.
The German's third victory in a row, and 22nd of his career, lifted Rosberg on to 273 points, eight clear of Hamilton, with six rounds remaining and Ricciardo a distant third on 179 in the title race.
Rosberg's win was his eighth of the season and first in Singapore, a grand prix that has only been won by world champions until now.
The German had started two points behind Hamilton and, despite leading comfortably halfway though the race, crossed the line just 0.488 seconds ahead of Ricciardo after having to complete the last 28 laps on the same soft tyres.
Red Bull opted for a bold tyre strategy to put pressure on Rosberg late on and Ricciardo was closing at roughly three seconds a lap in the closing stages but ran out of road before the chequered flag.
Hamilton had his own private battle with Ferrari's Kimi Raikkonen behind the leading duo, the Briton losing third place to the Finn after a mistake on lap 34 but reclaiming the position with a timely pit stop to hold on to the finish.
Last year's race winner Sebastian Vettel drove brilliantly from last place on the starting grid to claim fifth place in the other Ferrari, the German coming home ahead of Red Bull's Max Verstappen and Fernando Alonso in a McLaren.
The safety car was deployed immediately after the start when Nico Hulkenberg's Force India, eighth on the grid, suffered a heavy crash after making contact with Carlos Sainz's Toro Rosso.
Rosberg got away cleanly to lead from Ricciardo, with Hamilton in third and Raikkonen behind him after Verstappen suffered a woeful start to slip back to eighth from fourth on the grid.
The race restarted and Rosberg would have been startled to see a marshal at the end of the start-finish straight picking up debris, the man just managing to get off the circuit before the Mercedes reached him.
There were no more safety cars, throughout a 61-lap race that has yet to be completed without one, but the different tyre strategies of the leading cars made for a tactical and exciting race on a circuit that offers very few overtaking opportunities.