Vettel avoided all the trouble behind him at the first turn, and quickly established a comfortable lead.
Massa overtook Kobayashi after the first set of pit stops and managed to close the gap slightly, but Vettel maintained a strong lead to the checkered flag.
Vettel blocked Alonso during the final moments of qualifying on Saturday when the Ferrari driver was arriving at the chicane. Race officials reviewed the incident and reprimanded Vettel but allowed him to keep the pole. That decision may have been a factor in Alonso's aggressive start.
Sauber driver Sergio Perez's day came to an end when he spun off the track on the 19th lap trying to pass Lewis Hamilton at the hairpin turn. Perez will replace Hamilton next season at McLaren as the Briton moves to Mercedes.
With the winner decided early on, the focus for many of the fans became third place where Kobayashi was battling it out with Button, who won here last year.
Kobayashi, who started third, prevailed by half a second to become the first Japanese driver since Aguri Suzuki in 1990 to celebrate on the podium in front of the home crowd.
Hamilton finished in fifth, 20 seconds behind Button, and in front of a pack of cars fighting out the lower-point positions. Raikkonen took sixth ahead of Force India's Nico Hulkenberg, with Pastor Maldonado of Williams eighth and Webber recovering for ninth. Toro Rosso's Daniel Ricciardo held off Michael Schumacher of Mercedes to take the last point.
In the drivers' championship, Alonso and Vettel look like they'll be fighting it out for the title. Raikkonen is 33 points behind Vettel in third and five points in front of Hamilton. Webber and Button are 59 and 63 points off the lead, respectively.
Red Bull extended its lead in the constructors' championship to 42 points ahead of McLaren, with Ferrari another 20 points back.