The Red Bulls bolted after the safety car, lapping over a second quicker than third placed Alonso.
Hamilton was the first of those at the front to pit. He had spent the first stint behind Button who was much slower because he started on the harder tyres.
Once Hamilton had pitted, he put in a series of storming laps that meant he would likely clear Button when he stopped. Vettel and Alonso responded and pitted on the same lap, quickly followed by Webber.
At this stage, Button led the race, but it wouldn't be for long. He just didn't have enough pace, and was only a few seconds ahead of the Red Bulls anyhow.
After Button pitted for soft tyres he quickly caught Hamilton – who had slowed with a broken third gear – but never had the pace to challenge third place Alonso.
Michael Schumacher put in a good drive to finish sixth for Mercedes after team mate Nico Rosberg retired when the left rear wheel fell off his car.
Kamui Kobayashi finished seventh after passing at least five cars at the hairpin in dramatic moves, while Sauber team mate Nick Heidfeld finished in eighth.
Rubens Barrichello in the Williams and Sebastian Buemi in the Toro Rosso completed the points positions.
Provisional race results
Japanese Grand Prix; Suzuka, Japan; 53 laps; 307.573km
1. Vettel Red Bull-Renault 1h30:27.3232. Webber Red Bull-Renault + 0.9053. Alonso Ferrari + 2.7214. Button McLaren-Mercedes + 13.5225. Hamilton McLaren-Mercedes + 39.5956. Schumacher Mercedes + 59.9337. Kobayashi Sauber-Ferrari + 1:04:0388. Heidfeld Sauber-Ferrari + 1:09.6489. Barrichello Williams-Cosworth + 1:10.84610. Buemi Toro Rosso-Ferrari + 1:12.80611. Alguersuari Toro Rosso-Ferrari + 1 lap12. Kovalainen Lotus-Cosworth + 1 lap13. Trulli Lotus-Cosworth + 2 laps14. Glock Virgin-Cosworth + 2 laps15. Senna HRT-Cosworth + 2 laps16. Yamamoto + 3 laps17. Rosberg Mercedes + 5 laps
Fastest lap: Webber, 1:33.474
Sutil Force India-MercedesKubica Renault Hulkenberg Williams-CosworthMassa Ferrari Petrov Renault Liuzzi Force India-Mercedes Di Grassi Virgin-Cosworth
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