Lotus drivers Kimi Raikkonen and Romain Grosjean took second and third.
Sauber's Nico Hulkenberg fended off Mercedes' Lewis Hamilton for fourth.
Hulkenberg's presence in the top placings provided much of the excitement in the race and led to a frenetic last 20 laps after the field had been closed up following two safety-car periods.
Hulkenberg, who had spent the first part of the race defending from Alonso and Raikkonen, now found himself under intense pressure first from Hamilton and then from the Mercedes and Alonso, who also had McLaren's Jenson Button and Mercedes' Nico Rosberg close behind.
The Sauber was slow around most of the lap but fast on the straights and it led to some thrilling racing.
Hamilton actually passed Hulkenberg at Turn One on lap 48, with seven to go, but was re-passed down the straight to Turn Three. Meanwhile, Hamilton was also having to fend off Alonso.
Not long afterwards, Hamilton even got on the radio to his team to ask if anyone had any suggestions, a sentiment with which Alonso would have plenty of sympathy.
The Sauber's straight-line speed, and ability to come off Turn One faster than his rivals, meant Hulkenberg was able to hang on to fourth place.
“Great display under pressure. I know I sound like I've joined the Nico Hulkenberg fan club, but this is impressive”
David CoulthardBBC F1 co-commentator
BBC F1 co-commentator David Coulthard said: "Great display under pressure. I know I sound like I've joined the Nico Hulkenberg fan club, but this is impressive."
Hulkenberg had got himself into that position by making a good start from seventh on the grid and moving up to fifth on the first lap, passing Alonso after the Ferrari lost speed up the long straight after getting on to the kerb on the exit of Turn One avoiding Rosberg.
Vettel streaked away at the front, totally in control from lap one, while behind him Grosjean edged away from the Mercedes of Hamilton and Rosberg.
Vettel said: "Fortunately we had enough pace to get ahead after both safety cars but both Kimi and Romain were very competitive and did better with their tyres.
"I am really enjoying things at the moment, we have a great team and we are having a great time."
Hulkenberg held off Alonso and Raikkonen through the first pit stops before the Finn jumped ahead by bringing forward his second pit stop.
The race was then enlivened by two safety-car periods in quick succession.
The first was caused by a tyre failure on Sergio Perez's McLaren. At the re-start, Raikkonen passed Grosjean for second place into Turn One, despite a late defensive lunge by the Frenchman.
Grosjean said: "I made a small mistake and Kimi overtook me but it was my mistake. But we are back on the podium so it is all good."
But then the race had to be halted again after Mark Webber's Red Bull caught fire after being hit by the spinning Force India of Adrian Sutil at Turn Three.
Sebastian Vettel's pole lap in Korea
Hamilton had dropped from third to fifth as a result of his team leaving him out too long on a worn set of tyres before his second pit stop but after a brief dice with Alonso on the second re-start, the Mercedes driver set about his battle with Hulkenberg.
At the front, Vettel was serenely coasting home to his fourth straight win, his only concern the wear on his right front tyre, the same tyre that had failed on Perez's car.
Behind him, Grosjean had been urged to race Raikkonen, being told by the team he was faster than the Finn, but was unable to get close enough to try.
Rosberg took seventh, delayed by a front wing failure mid-race, ahead of Button and Ferrari's Felipe Massa.
Marussia's Jules Bianchi and Caterham's Charles Pic have been given 10-place grid penalties for the Japanese Grand Prix after receiving their third reprimands of the season.
Both drivers were adjudged to have failed to slow down sufficiently for yellow flags during the race.
Caterham's Giedo van der Garde and Marussia's Max Chilton picked up their first reprimands of the season because they failed to stay above the minimum time set by the FIA during a safety car period.
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