Rosberg led the title race by 43 points earlier in the season and is looking to follow his victories in Belgium and Italy in the last two races with a maiden triumph around the Marina Bay street circuit.
There had been fears the Mercedes would be off the pace after struggling and failing to make the podium in Singapore in 2015.
But Rosberg put any fears that he would be outpaced by Red Bull or Ferrari firmly to bed with a blistering lap to pile pressure on his team-mate Lewis Hamilton, whose lead has been reduced to two points.
Rosberg scorched round the Marina Bay circuit in 1min 42.584sec, more than half-a-second quicker than Red Bull's Daniel Ricciardo's 1:43.115, with Hamilton only managing 1:43.288 for third place.
Red Bull's Max Verstappen was fourth, but last year's winner Sebastian Vettel had a qualifying nightmare in his Ferrari, as a broken anti-roll bar relegated him to the back row of the grid.
Rosberg has never been on the podium in Singapore but he will now be hopeful of celebrating his 200th grand prix by overhauling Hamilton on Sunday.
"Definitely happy with that one for my 200th grand prix," beamed Rosberg after qualifying.
The German driver finished fourth in Singapore a year ago but is in the ascendancy after his back-to-back wins at Spa and Monza. He described his run to pole as "one of my top three laps ever".
Hamilton has work to do in Sunday's race on a circuit which is notoriously difficult for overtaking.
Six of the eight runnings of the race to date have been won from pole position. "I like that statistic," Rosberg said.
Red Bull lived up to the pre-qualifying predictions by proving to be Mercedes' nearest challengers as Max Verstappen joined Hamilton on the second row of the grid.
Tyre strategy could be key on the bumpy, twisty street circuit which feature 23 corners, more than any other track on the current Formula One calendar.
Ricciardo and Verstappen will start on the longer-lasting supersoft tyres that they used in Q2, while Mercedes will utilise the sticky ultrasofts.
The ultrasofts are quicker but have a question mark over their race endurance as they are being used in Singapore for the first time.
"If we can get the start we want I think we can control the situation tomorrow," said Ricciardo
"But it's not a predictable race. There are normally incidents and safety cars so it won't be straightforward."