Australian team mate Mark Webber bowed out of Formula One with second place, anchoring a Red Bull one-two in his 215th and final race for the champions before heading to Le Mans sportscars with Porsche.
Ferrari's Fernando Alonso, this season's overall-runner-up, finished third on a day when the skies over Interlagos failed to deliver the rain that had forced delays to qualifying on Saturday.
Vettel is the first Formula One driver to win nine successive races in a single season although Italian Alberto Ascari strung together nine in a row over two campaigns in 1952-53.
"Guys, I am so proud of you. I love you. Remember this, enjoy this moment. Yes. We did it. This is unbelievable," the 26-year-old German said, his voice wavering over the team radio after he took the chequered flag.
Vettel's victory equalled compatriot Michael Schumacher's 2004 record with Ferrari of 13 wins in a season.
"I am actually quite sad that this season is coming to an end," he said in a podium interview after he and Alonso had doused Webber, who ends the year third in the championship, in champagne.
Vettel and Red Bull had secured their fourth successive drivers' and constructors' titles in India last month.
Jenson Button, the 2009 world champion and last before Vettel, finished fourth for McLaren - a result that rescued the team from suffering their worst season since their debut in 1966 even if they failed to stand on the podium at any point in 2013.
Nico Rosberg was fifth for Mercedes, who end the championship as overall runners-up and six points ahead of Ferrari.
Mexican Sergio Perez was sixth, after starting 19th following a five place grid penalty, in his final appearance for McLaren with his future uncertain.
Brazilian Felipe Massa, angry and incredulous after being handed a drive-through penalty, brought down the curtain on eight years as a Ferrari driver with seventh place in front of his home fans.
Mercedes's Lewis Hamilton was ninth and was also handed a drive-through penalty for a coming together with Finland's Valtteri Bottas that left the Briton limping back to the pits with a puncture while the Williams shed a rear tyre and retired.
Marussia won the battle with Malaysian-owned Caterham for 10th place in the constructors' championship - a position with considerable financial implications for both with only the top 10 getting a share of the revenues.
(Writing by Alan Baldwin in London, additional reporting by Tatiana Ramil, editing by Tony Jimenez and Toby Davis)
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