Vettel, driving for Red Bull Racing-Renault, was in 17th place after a very early pit stop for a change of tires but steadily moved up and was in second to teammate Mark Webber by the 21st lap. Seven laps later, Webber was in the pits and Vettel in front for good.
He completed the 60-laps around the 3.19-mile Buddh International Circuit in 1 hour, 31 minutes, 12.187 seconds. Vettel has won the Indian Grand Prix all three years it's been run.
Nico Rosberg, in a Mercedes, was second 29.8 seconds back of Vettel while Romain Grosjean, driving for Lotus-Renault, was another 10 seconds behind. Ferrari's Felipe Mass was fourth and Sergio-Perez, on the McLaren-Mercedes team, came in fifth.
It was the sixth consecutive Grand Prix win this year for Vettel, who earlier in the season won four times. He has amassed 322 points in the drivers' standings and joins Juan Manuel Fangio, Alain Prost and Michael Schumacher as the only men to win four Formula 1 drivers' championships.
Vettel has 36 Grand Prix wins in his career, which is fourth most behind Schumacher (91), Prost (51) and Ayrton Senna (41).
Fernando Alonso, who was 11th Sunday in his Ferrari, is second in the 2013 drivers' standings with 207 points and Lotus-Renault's Kimi Raikkonen is third with 183. Lewis Hamilton, with Mercedes, ranked fourth at 169 and Webber is fifth at 148.
There are three races left on the 2013 Formula 1 calendar with the Nov. 3 Abu Dhabi Grand Prix next up.