The 25-year-old German, who was involved in an opening lap collision with Williams' Bruno Senna yesterday, which sent him to the rear of the field, made light of the damage to his Red Bull car as he fought back in a dramatic race run in treacherous rain-swept conditions at the Interlagos circuit.
Vettel's only title rival, two-time champion Spaniard Fernando Alonso, finished a fine second after a courageous drive for Ferrari, but it was not enough to overhaul a pre-race 13-point deficit as his German rival won the crown by just three points.
The race was littered with accidents and incidents and ended behind a safety car with Vettel bringing his car home in the rain in tears, unable to respond to the screamed congratulations from Red Bull team chief Christian Horner.
"This is really special. Right to the end I didn't know if I'd done enough. Trundling along behind the safety car and then dragging over the line was just torture," said Vettel.
Regarding his early collision which so nearly wrecked his race Vettel said: "I just kept trying to race. We always believed.
"I was so very happy to climb back after being hit like that at the start -- you imagine spinning backwards on the M25 (British motorway)... Not a very comfortable feeling.
"I really want to thank everyone in the team here and in the factory and all of us. Nobody feels more important than anybody else. It is unbelievable for me."
"I had to avoid everyone and I was lucky nobody hit me. Fortunately, the front wing was intact which was important. I forced back and in the mixed conditions I was the slowest car out there on the straight.
"We just did our thing. That's the way we do it and it works in our team," Vettel said.
"To do this, for all of us in the team it is unreal... also to win a third title here, where one of the greatest Ayrton (Senna) came from..."
"Christian came on the radio and told me the names of all the three-times champions and I cried."
Vettel became only the third driver in history to win three successive titles, equalling the feats of the great Argentine Juan Manuel Fangio and childhood idol Michael Schumacher, who finished seventh for Mercedes in his final race before retiring.
Alonso's Ferrari team-mate, local hero Brazilian Felipe Massa, drove brilliantly to finish third ahead of Australian Mark Webber in the second Red Bull and German Nico Hulkenberg of Force India.
"We lost communication at the start but Sebastian stuck at it. He drove with determination," said Horner.
"He just never gives up. After the first lap spin I thought that was it because we knew Fernando would be on the podium. But he got back to the top six, the rain came, we went to inter (tyres) and then slicks.
"It was maximum stress throughout the race, but Seb stayed cool. Fernando did a great job but he knew he was up against one of the best. What Seb achieved was incredible."
Hulkenberg played a prominent role in the race, not only leading for a spell but also crashing into Lewis Hamilton's McLaren to wreck the Briton's hopes of a triumphant conclusion to his career with the British team just when he looked sure of winning.
Vettel was sixth, Schumacher seventh and Frenchman Jean-Eric Vergne eighth for Toro Rosso ahead of Japan's Kamui Kobayashi of Sauber and Finn Kimi Raikkonen of Lotus.
Vettel, whose Red Bull team took a third constructors' championship in succession last weekend in Texas, finished with 281 points and Alonso with 278.
"First of all I'm very proud of the team. We lost the championship before today, not in Brazil, this is a sport after all," said Alonso.
"When you do something with your heart and do it 100 percent you have to be proud of yourself and your team and we'll try again next year."
It was Button's first win in Brazil, his third of the season and the 15th of his career.
"First of all I want to congratulate the whole team. This is the perfect way to end the season. We have had ups and downs and to end on a high bodes well for 2013," said the McLaren driver.
In the emotional build up to a race of farewells and coronations, Schumacher did a lap in his Mercedes, carrying a flag to thank his fans.
"It was very emotional for me, but I wanted to share my passion," said the veteran seven-time world champion.
Massa said: "The second part of the year was preparation for next year. It was so emotional to race here and I think the race was fantastic.
"For sure, it could have been a better position than I finished but I don't know what to say or feel. I just started crying, it is so amazing."