Vettel, driving for Red Bull Racing-Renault, moved away quickly in the first lap and was in control from there, despite minor issues with his tires. He finished the race in 1 hour, 43 minutes, 13.7 seconds, about 4 seconds ahead of Lotus's Kimi Raikkonen with Romain Grosjean, also in a Lotus, about 5 seconds off Vettel's pace.
It was the third time in the four years the Korean Grand Prix has been run that Vettel won the race. He led virtually all of the 55 laps Sunday around the 3.48-mile Korea International Circuit.
The win in Korea marked the fourth straight Grand Prix victory for Vettel, who won recently in Belgium, Italy and Singapore. It was his eighth Grand Prix win this year and 34th in his career. Only three drivers have won more Formula 1 races than Vettel.
He has 272 points in the drivers' standings, comfortably ahead of Ferrari's Fernando Alonso, who is second with 195 points. Raikkonen is third at 167 and Lewis Hamilton, who drives for Mercedes, is fourth with 161.
Vettel could secure the 2013 drivers' championship if he wins next week's Japanese Grand Prix, where he's won three of the last four years, and Alonso ends up lower than eighth. Counting the race in Suzuka, Japan, there are five races on the 2013 Formula 1 calendar.