The 23-year-old Red Bull driver started from the pole trailing Alonso by 15 points in the standings. While Vettel had a fairly trouble-free race, Alonso finished seventh after Ferrari made an ill-advised decision to pit early and the Spaniard got stuck behind Nico Rosberg and Vitaly Petrov for nearly 40 laps.
"It has been an incredible journey, to lead the championship after the last race is unbelievable," Vettel said. "It's been extremely intense, and a tough season mentally."
The German is six months younger than Lewis Hamilton was when he won the title in 2008.
Vettel's championship caps a season in which Red Bull regularly dominated the field in qualifying, but often failed to convert its unrivaled speed into race victories because of reliability problems and driver errors.
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