The German, starting from pole, fought off Nico Rosberg in the first corner and despite a safety car intervention, he was untouchable as he scored his third win in a row and a hat-trick of wins in Singapore.
Ferrari’s Alonso finished second to keep up the title pressure on Vettel, who now leads the championship by 60 points from the Spaniard with six races remaining.
Lotus driver Kimi Raikkonen braved back pain to finish third but there was disaster for Red Bull’s Mark Webber, whose late charge ended in a blown engine and a ride back to the pits on the wing of Alonso’s Ferrari.
Mercedes’ Nico Rosberg and Lewis Hamilton claimed fourth and fifth, Ferrari’s Felipe Massa was sixth and McLaren pair Jenson Button and Sergio Perez occupied eighth and ninth.
But yet again the race belonged to Vettel, who was literally streets ahead of his rivals on the spot-lit Marina Bay circuit through the highways of downtown Singapore.
“The start was quite hairy, Nico had a better start and I didn’t get going,” said Vettel. “But unfortunately he went a little too deep and I could get it back.
“With the safety car it was difficult but as soon as the safety car came off we had very strong pace with the car. It was just a pleasure to drive around this crazy race.”
The peerless 26-year-old has now won four of the last five grands prix and is a racing certainty to become the sport’s youngest four-time world champion, joining Michael Schumacher and Juan Manuel Fangio as only the third man to win four in a row.
From the start, Rosberg arrowed past pole-sitter Vettel going into the first turn but his speed carried him wide at the second corner and the Red Bull man was able to nip back in front.
Behind them, Alonso pulled off a masterful move as he used the outside of the track to leap from seventh on the grid to third in the opening seconds.
Hamilton passed Massa illegally and had to give back the spot after a sharp warning from his team over the radio.
But as the cars started to string out, it was all about Vettel as he hared off in front in his customary fashion, establishing a seven-second lead by lap seven.
As the cars behind him garaged for medium tyres, Vettel strung out his lead to 36 seconds and he was able to pit on lap 17 and still maintain an eight-second lead over Rosberg.
Force India’s Paul Di Resta nipped in behind Rosberg for third place during the pits shake-up, frustrating Alonso who was unable to pass and challenge for second.
By lap 25 of the 61, Vettel was nearly 11 seconds ahead when Daniel Ricciardo, heading to Red Bull next year, ploughed into the barriers at turn 18 and totalled his Toro Rosso.
The safety car roared out, erasing Vettel’s lead but when it disappeared five laps later, it was deja vu as the German shot out to a 3.2-second lead on the first trip round the circuit.
And Vettel showed sheer class again as he scorched to the race’s fastest lap and then powered out to a 12-second lead by lap 35.
Lotus’s Romain Grosjean cried “No!” over the radio as his team pulled him in over a hydraulics problem which prompted a lengthy stay in the pits, and then a frustrating retirement.
Two more fastest laps and the incredible Vettel had stretched his lead to more than 20 seconds by circuit number 39, before coming in for his second and final tyre-change a few laps later.
He emerged comfortably ahead of the wily Spaniard Alonso and with 10 laps to go, the lead was pushed to more than 10 seconds as Vettel zeroed in on his seventh win of the season.
The real battles were in his rear-view mirror, as Webber squeezed up inside Hulkenberg to take sixth and Raikkonen pulled off a peach of a move outside Button for third.
Paul Di Resta ploughed his Force India into a wall but crucially, there was no safety car and Webber slipped past Perez and then Button to move into fourth.
It was building into a titanic finish until smoke started pouring from the despairing Webber’s engine and he eventually had to abandon his fiery Red Bull and hitch a ride with Alonso.
Meanwhile Vettel was already celebrating as he heads towards another world title and a place among the sport’s greatest names.