The 24-year-old German, the defending champion and runaway leader of this year's one-man title race, drove from pole position to the chequered flag in flawless style in his Red Bull Racing car.
He won the floodlit 61-lap night race at the Marina Bay street circuit by a controlled 1.7 seconds.
Vettel now requires a solitary point to claim his second title in succession and can only be beaten to the crown if Button wins all the remaining races while the German fails to score a further point.
With the next race the Japanese Grand Prix October 7-9, there is every chance the peerless Vettel will seal his triumph -- and make history -- at the Suzuka circuit.
"Obviously I am very pleased with the result and the car was great for me all the way through. I pulled away easily at the start and had a good gap, but the safety car was not in our plans," said Vettel. "I was lucky again to have a good re-start and I was soon back in the rhythm and I had a huge gap again, even with the traffic.
"I was in control at the end and it is a great feeling to win this race -- I love the track here and it's such a challenge.
"As to the championship? Ah, well, I guess I have another chance at the next race."
Button revealed his frustrations with slower rivals on the Singapore circuit, which is notoriously hard to overtake on.
"I can understand that's it's difficult to move over here and most people are fighting out there, but the backmarkers have got to respect that the cars that are lapping are lapping for reason," said the Briton, who became world champion in 2009.
"I feel like I got everything out of the car, especially in the last part of the race, I was able to push on tyres to see what the car had. We weren't quick enough to win today, but it's something to build on."
Two-time world champion Spaniard Fernando Alonso, who needed to finish on the podium to keep his own challenge for the drivers' title alive, came home fourth ahead of Briton Lewis Hamilton in the second McLaren.
Hamilton produced a typically spectacular drive including five pit-stops, a collision and a charge from 16th through the field.
Another Briton, Paul Di Resta, came home sixth for Force India, his best result to date in his rookie season in Formula One, ahead of Germans Nico Rosberg in seventh for Mercedes and Adrian Sutil in the second Force India.
Felipe Massa of Ferrari, who was the victim of a collision with Hamilton in the early stages of an incident-filled contest, came home ninth.
Mexican Sergio Perez, whose collision with Michael Schumacher saw the German eliminated from the race, finished 10th.
It was Vettel's ninth win this season and the 19th of his career. His Singapore triumph in sweltering humidity was heralded by an explosion of dazzling fireworks over the brightly lit cityscape.
Vettel won in a victorious time of one hour, 59 minutes and 6.757 seconds, a time that signalled the longest and most arduous race of the year.
He, Button and Webber stood still, drained and dripping with sweat on the podium at the end.
Vettel, from his 11th pole position, pulled clear with apparent ease to take control early on, leaving the rest to scrap for places in a flurry of action into Turn One, Sheares Corner.
He stretched his lead to 20 seconds by lap 30, when the race was red-flagged for the first time after Schumacher ran into the rear of Perez's Sauber car and made an airborne collision with the barriers.
This brought out the safety car and signalled a spate of pit-stops while Schumacher's wrecked Mercedes was lifted clear. The 42-year-old German was unhurt.
It gave Button a sniff at Vettel, and although he ran him close he never looked like denying the German the victory he deserved.