Vettel led all 53 laps for his third win of the season. He gained nine points on current title leader Button with two races remaining in the season -- in Brazil and Abu Dhabi.
"It can still be done," Vettel said. "It is looking much better now. It would be nice to have a couple more races left, but two races to go ... We are here to fight, and the best thing we can do is win like we did."
Despite an eighth-place finish, Button left Japan with a 14-point advantage over Barrichello and a 16-point lead over Vettel.
In 2007, Lewis Hamilton held a 17-point advantage over Kimi Raikkonen heading into the final two events of the season. Raikkonen won the Chinese and Brazilian Grand Prix and won the championship by a single point.