The German pulled away initially at a second a lap but 2009 champion Button reined him in and took the lead at his second pitstop when he emerged just ahead of the German in a race dictated by tyre wear.
"I think we were a little bit too weak today on the option tyre," said Vettel, who has been otherwise dominant in his charge to the title after seizing his first against the odds in the final race last year.
"To win the championship here is fantastic. So many things you want to say in this moment but it's hard to remember all of them," he added. "There are so many people, it's hard to name them all to thank them."
A safety car incident triggered by another coming together between McLaren's Lewis Hamilton and Ferrari's Felipe Massa, as well as a contact between Red Bull's Mark Webber and Mercedes' Michael Schumacher, bunched up the field for three laps while marshals retrieved debris.
Button kept his lead and took the chequered flag for what he considers a second home race, thanks to his Japanese girlfriend and long-standing passion for the country, just 1.1 seconds over Alonso.
Image: Red Bull Formula One driver Sebastian Vettel of Germany celebrates in front of team members after finishing third in the Japanese Grand Prix to clinch the Formula One drivers championship, at the Suzuka Circuit in Suzuka, Japan on Sunday, Oct. 9, 2011.