The final laps were enlivened by close battles between a number of drivers as those who chose not to stop during a mid-race safety-car period but make their final pit stops later closed on those who had stopped during the caution period.
But ahead of the late excitement, Vettel was in a race of his own, able to lap at a pace far beyond any of his rivals.
The Mercedes, second on the grid, nosed ahead into Turn One, despite Vettel leaning on him down the pit straight, but Rosberg ran wide through Turn Two and Vettel was able to sneak back ahead.
What makes Singapore so spectacular?
Vettel proceeded to streak away at the front in trademark style, building a 5.6-second lead in just three laps before being told to back off slightly to manage his tyres.
Despite that, he continued to extend his lead, taking it out to 8.2secs before his rivals behind him started to make their first pit stops.
Vettel was in total control when the safety car was deployed on lap 25 of 61 after Toro Rosso's Daniel Ricciardo crashed into the barriers at Turn 18.
His true superiority was demonstrated at the restart on lap 31, when Vettel was told to push to the limit to build a gap.
His pace was breathtaking - from building a 3.2-second lead over Rosberg after just one lap, he was 10 ahead after four and 22 ahead after 10. "It was mind-blowing," said BBC F1 technical analyst Gary Anderson.
Vettel was able to make his final pit stop without losing the lead and controlled the race to the end.
The German made a joke about being booed again on the podium, which is becoming routine.
A safety car has been deployed for every Singapore GP since the inaugural 2008 race
"They are on a tour - they go around on a bus," he said with a smile.
Vettel added: "The start was quite hairy, Nico had a good start - better than me. I didn't get going initially, but fortunately he went in a little bit deep and I could get him back, which was crucial as we had very good pace."
The battling all took place behind the German and his peerless car.
Rosberg held on to second place in the early laps from Alonso, who made a typically stunning start from seventh on the grid to be third on the exit of the first sequence of corners on the first lap.
Alonso looked like he might have a chance of leap-frogging Rosberg at the first stops, only for a slow stop to leave him stuck behind Paul Di Resta's Force India when he needed clear air to benefit fully.
When the safety car was deployed, Alonso and Ferrari gambled on making a pit stop and trying to run to the end without stopping again.
The decision lost him places to Webber and Hamilton, who like Vettel and Rosberg in first and second places chose not to stop under the safety car.
Alonso assumed second place when his rivals stopped and they were unable to make up the ground, ensuring the Spaniard limited the damage he suffered in the championship as much as possible.
"It was a fantastic start, we knew we didn't have the pace today, we had to invent something," said Alonso. "It was a very good strategy and it paid off with a second place, which tastes like a victory to us.
Alonso vows to keep fighting for title
"It was a risky move, but we are second in the championship and we have to gamble. They were too fast all weekend, we have to congratulate them on a fantastic weekend and next time we have to do better."
Lotus's Romain Grosjean, who qualified third but dropped to fifth at the start, was right behind Alonso at the re-start and looked to have a shot at second place but was forced to retire with a lack of engine air pressure.
That promoted Button and Raikkonen, who also stopped under the safety car, to third and fourth.
With 10 laps to go, Button looked like he might be able to score McLaren's first podium of the year, but he fell back to seventh at the end as his tyres ran out of grip.
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