Germany's Vettel was first to spot the man and had the presence of mind to radio in to his team. "There is a fan on the track," he repeated twice.
It led to a second safety car at two thirds distance of the 61-lap race on the Marina Bay circuit.
F1 officials later said that a 27-year-old man had been arrested and that the incident was being investigated.
After the safety car pulled off, Vettel powered clear again to win from Red Bull's Daniel Ricciardo and his Ferrari teammate Kimi Raikkonen. Nico Rosberg was fourth.
With title leader Lewis Hamilton forced to retire in his Mercedes with a mystery technical issue, Rosberg closes the gap on his teammate to 41 points, with Vettel reviving his title hopes a further eight points back.
Hamilton had come to the night race hoping to draw level with his hero Ayrton Senna on 41 Grand Prix victories, but after only qualifying fifth was unable to make much impression before his race ended early just after halfway.
Instead, Vettel took the plaudits and moved one clear of Senna to third on the all-time list with his 42nd F1 career win, a result never in doubt after making a clean start from pole.
The only hurdles were the safety cars, the first coming after 15 laps following a collision between the Williams of Felipe Massa and Nico Hulkenberg in the Force India.
Each time, Vettel was able to distance Australia's Ricciardo for his third win of the season for the Prancing Horse team and with six races to go of the 2015 season has an outside chance of a fifth world title.
"We still have a small chance. Maybe we can make the impossible possible," Vettel said at the victory celebrations.
Behind the main title contenders, there was a superb but in the end controversial drive by 17-year-old Max Verstappen who carved his way through the field from the back of the grid to finish eighth, but defied an order from his Toro Rosso team to allow teammate Carlo Sainz past in the closing stages.
Only 14 cars finished the floodlit race on a technical street circuit which tests drivers and cars.