Vettel, who had already secured the Formula One title, still finished second after letting Webber pass him almost halfway through the race at the 2.6-mile Interlagos track.
Jenson Button of McLaren finished third to secure second place in the drivers' standings.
Webber easily passed Vettel on lap 30 after his teammate reduced his pace after being told by the team that there was something wrong with his gearbox.
"Very early I got the call that we had to manage the gearbox problem," Vettel said. "It sounded pretty severe. It started to get worse. My main priority was to finish the race."
Webber finished third in the championship, helped by his first victory of the season. It was his seventh overall in F1, and the second in Brazil after winning in Interlagos in 2009.
"Today was a good grand prix for me. It's not a bad thing to finish the year like this," Webber said. "I felt good all weekend. It would have been nice to have a race all the way through (with Vettel) but he had a bit of a problem."
Vettel, last year's winner in Brazil, had 11 victories this season. But he was shut out in the final two races. He retired on the first lap in Abu Dhabi because of a puncture.
Vettel's second-place finish came a day after the two-time champion captured his 15th pole of the season to break Nigel Mansell's 19-year record. The 24-year-old German had clinched the title four races ago, at the Japanese GP.
"I think we had a pretty amazing season and it would be over the top being upset now," Vettel said. "So we take the second place, the 1-2 finish for the team, which is great."
Red Bull also had already won the constructors' championship, with McLaren finishing second and Ferrari third.
On a dry track despite forecasts of rain, Webber took the lead when Vettel gave his teammate plenty of space at the end of the main straight.
Red Bull told Vettel on lap 14 that data from his car showed a gearbox problem and asked him to short shift when in second gear. The problem then got worse and the team later said Vettel had to short shift in every gear, considerably slowing his lap times.
After Webber got past, Vettel again increased his pace and had no problem staying behind his teammate.
Vettel dismissed suggestions that team orders may have come into play to try to help Webber finish second in the points standings.
"We had no choice," Vettel said. "More and more I was forced to slow down and at the end I was not using second gear."
Lewis Hamilton, the winner in Abu Dhabi two weeks ago, also had a gearbox problem with his McLaren and eventually retired on lap 48.
Seven-time champion Michael Schumacher of Mercedes punctured his left-rear tire while trying to pass Bruno Senna of Renault at the end of the main straight. Schumacher had already passed Senna when the Brazilian's car touched his tire and forced him to make an unscheduled pit stop that led to a 15th-place finish.
Senna also had to make a stop because of damage to his car and eventually received a drive-through penalty for the incident and finished 17th.
Veteran Brazilian driver Rubens Barrichello, who is yet to secure a drive for next year and could have made his last F1 race after an 18-year career, got off to a slow start from 12th position and finished 14th.
Timo Glock of Virgin had a tire come off his car after a pit stop and he had to retire at the exit of the pit lane on lap 23.