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The unstoppable German, 26, could retain the title in Japan next week if he wins and Ferrari rival Fernando Alonso finishes outside the top eight.
Not even two appearances by the safety car, or the worrying sight of his team-mate Mark Webber climbing out of his burning Red Bull, was enough to stop Vettel's fourth win on the bounce.
He took the chequered flag 4.224sec ahead of Kimi Raikkonen of Lotus, who just beat team-mate Romain Grosjean -- told by his team to "smile on the podium" -- to the line for second.
Sauber's Nico Hulkenberg and Mercedes' Lewis Hamilton, who started second on the grid, were fourth and fifth.
Vettel's third win on the trot in Korea means he has racked up 272 points, a mammoth 77-point lead over nearest challenger Alonso, who came home sixth at Yeongam, with five races to go.
"I'm loving what I do," Vettel, booed at previous races because of his dominance, told the crowd from the podium.
"I'm trying not to think about it to be honest," Vettel told a post-race press conference, flanked by Raikkonen and Grosjean, when reminded he could win the title next week at Suzuka.
"There are still a lot of points to get even though it looks very good for us. There is a chance for Fernando (Alonso) so we need to stay on top of our game.
"To be honest, as I said on the podium, we are just having a good time. We enjoy the fact the team is working very well, the car is working -- it's very on the edge... probably more than you think from the outside."
The real battle on an overcast but dry afternoon next to the Yellow Sea was behind the German, with Hamilton and Grosjean duelling for long periods for second.
Hamilton's Mercedes team-mate Nico Rosberg was also in the mix before a problem with his wing saw sparks dance spectacularly from the belly of his car as he overtook Hamilton mid-race.
An extended pit stop saw the German rejoin in midfield and he had to settle for seventh, with McLaren's Jenson Button eighth.
Felipe Massa of Ferrari and Sergio Perez of McLaren rounded out the top 10.
Ferrari-bound Raikkonen, who started back on ninth on the grid but battled his way through with a superb exhibition of aggressive racing, said: "I think I lost a place on the first straight.
"The car has been under-steering this weekend and was doing it today and I had to look after my front tyres.
"I got stuck in traffic but even without the safety car we could have finished on the podium."
Vettel was already streaking away at the first hairpin, where there was early drama when Massa spun around, causing his team-mate Alonso to run wide with Button and the Force India of Adrian Sutil suffering minor damage.
The Brazilian Massa, who started sixth on the grid, found himself dumped down to the back of the field.
There was another hair-raising incident on lap 31, when Perez saw a front-right wheel explode on the straight, catapulting rubber dangerously over the track and bringing out the safety car.
But no sooner had the safety car departed than it was back out on lap 38 when Sutil was again in the thick of it, appearing to spin and take out Webber.
The Australian's Red Bull glided off the circuit and went up in flames, but Webber -- who qualified third but started 13th on the grid because of a penalty -- clambered out safely.
"It's not great getting stuck behind the safety car, but I'm really pleased with the result and great by the team," said a delighted Vettel, who never looked in danger of relinquishing his spot at the front.
"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," he added.
Results from the Korean Grand Prix on Sunday:
1. Sebastian Vettel (GER/Red Bull Racing), 1h 43mins 13.701sec
2. Kimi Raikkonen (FIN/Lotus) at 4.224
3. Romain Grosjean (FRA/Lotus) at 4.927
4. Nico Hulkenberg (GER/Sauber) at 24.114
5. Lewis Hamilton (GBR/Mercedes) at 25.255
6. Fernando Alonso (ESP/Scuderia Ferrari) at 26.189
7. Nico Rosberg (GER/Mercedes) at 26.698
8. Jenson Button (GBR/McLaren Mercedes) at 32.262
9. Felipe Massa (BRA/Scuderia Ferrari) at 34.390
10. Sergio Perez (MEX/McLaren Mercedes) at 35.155
11. Esteban Gutierrez (MEX/Sauber) at 35.990
12. Valtteri Bottas (FIN/Williams) at 47.049
13. Pastor Maldonado (VEN/Williams) at 50.013
14. Charles Pic (FRA/Caterham) at 1:03.578
15. Giedo van der Garde (NED/Caterham) at 1:04.501
16. Jules Bianchi (FRA/Marussia) at 1:07.970
17. Max Chilton (GBR/Marussia) at 1:12.898
18. Jean-Eric Vergne (FRA/Scuderia Toro Rosso) at 2 laps
19. Daniel Ricciardo (AUS/Scuderia Toro Rosso) at 3 laps
20. Adrian Sutil (GER/Force India) at 5 laps
Reasons for retirements:
Paul di Resta (GBR/Force India): accident, 25th lap
Mark Webber (AUS/Red Bull Racing): accident, 37th lap
Overall standings:
Drivers:
1. Sebastian Vettel (GER) 272.0pts, 2. Fernando Alonso (ESP) 195.0, 3. Kimi Raikkonen (FIN) 167.0, 4. Lewis Hamilton (GBR) 161.0, 5. Mark Webber (AUS) 130.0, 6. Nico Rosberg (GER) 122.0, 7. Felipe Massa (BRA) 89.0, 8. Romain Grosjean (FRA) 72.0, 9. Jenson Button (GBR) 58.0, 10. Paul di Resta (GBR) 36.0, 11. Nico Hulkenberg (GER) 31.0, 12. Adrian Sutil (GER) 26.0, 13. Sergio Perez (MEX) 23.0, 14. Daniel Ricciardo (AUS) 18.0, 15. Jean-Eric Vergne (FRA) 13.0, 16. Pastor Maldonado (VEN) 1.0
Constructors:
1. Red Bull Racing 402.0pts, 2. Scuderia
Ferrari 284.0, 3. Mercedes 283.0, 4. Lotus 239.0, 5. McLaren Mercedes
81.0, 6. Force India 62.0, 7. Sauber 31.0, 8. Scuderia Toro Rosso 31.0,
9. Williams 1.0
