Vettel's Australian team-mate Mark Webber was third. It was just the fourth time in the history of the Formula One World Championship that all the drivers finished the race and first time in 46 years.
Great Britain's 2008 champion Lewis Hamilton for McLaren honoured his pledge to restrain his daredevil style and finish the race, taking fourth place.
Brazilian Felipe Massa in the second Ferrari and Briton Jenson Button, in the second McLaren, finished fifth and sixth.
German Nico Rosberg was seventh for Mercedes and Spaniard Jaime Alguersuari produced a stunning drive to take eighth for Toro Rosso with Germans Adrian Sutil ninth for Force India and Nick Heidfeld 10th for Renault.
No pressure "Ooooooh yes, baby!" screamed Vettel over his team radio after winning.
"That is better than anything you can imagine this year. Yes. Yehhhh!
Vettel, whose other two finishes this year were as runner-up, produced the perfect riposte to those who felt he might buckle under pressure.
Vettel and the Red Bull RB7 have consistently been the fastest driver-car combination in dry conditions this year.
However, starting from the next race at Silverstone, F1’s governing body will be heavily restricting the amount of exhaust gases that can be passed from a car’s engine to it’s diffuser. There is speculation that this rule change could slow Vettel and Red Bull down.