Mark Webber benefited from teammate ending Brazilian Grand Prix.
Vettel, the two-time Formula One world champion, started on the pole for a record 15th time this season and led in the early going of the 71-lap race at the 2.677-mile (4.309-kilometer) Interlagos circuit. But Vettel was informed by his Red Bull team of the gearbox issue. The team instructed him to short- shift in second.
Shortly after Vettel was told the gearbox problem was getting worse, Webber easily passed his teammate on lap 30 and took command from there. Webber claimed his seventh career F1 win, but his first since August 2010 in the Hungarian Grand Prix (26 races ago).
"It would have been nice to have a race with Sebastian all the way through, but he had a little bit of a problem," Webber said. "It's a win which you will take for sure, because I've had enough bad luck or whatever you want to call it. That's how it goes sometimes. It's a very important win for me and the team to finish on a high."
Webber also won the Brazilian GP in 2009.
Vettel, who won the Brazilian GP last year, nursed his car to a second-place finish. Two weeks ago, Vettel suffered a flat tire and spun out on the opening lap of the Abu Dhabi Grand Prix. He sustained suspension damage and ended up finishing 24th.
"It was a real shame, because I had a good start and a very good feeling," Vettel said. "I got the call very early on that I had to manage the gearbox problem. I had to turn down the engine and short-shift. It was getting worse throughout the race, so I ended up using higher gears."
Vettel concluded his second consecutive championship season with 11 wins and 17 podium appearances in 19 rounds. He also accumulated a whopping 392 points for the season.
"Choosing to put the harder tire on for the last two stints worked pretty well for me," Button said. "Fernando struggled on the harder tires, and I was able to make the pass near the end but third was as high as I could get."
Webber's win coupled with a fourth-place finish for Alonso allowed Webber to secure the third position in points, only one marker ahead of Alonso.
Brazilian Felipe Massa drove his Ferrari to a fifth-place run in front of his home crowd.
Sauber's Kamui Kobayashi and Vitaly Petrov from Renault completed the top-10.
Lewis Hamilton, who won at Abu Dhabi, also suffered a gearbox problem in the Brazilian GP, which ended his race on lap 47. The McLaren driver finished 22nd.
"I had a gearbox problem occur quite early on, and I was having problems with the gear shifts between first and second," Hamilton said. "With that, I was losing quite a lot of time, and eventually, the gearbox just gave up."
Hamilton ended his season fifth in the championship standings, 30 points behind Alonso.