The 24-year-old German, who clinched back-to-back drivers' title in Japan last weekend, took the lead from McLaren's Lewis Hamilton on the opening lap and never looked back despite a safety car period bunching up the field.
With three races remaining, and a maximum 129 points to be won, Red Bull have an insurmountable 140-point lead over McLaren.
Vettel's 20th Formula One victory left him three off seven times champion and compatriot Michael Schumacher's 2004 record of 13 wins in a single season with Ferrari.
"Yes, yes, yes. Ten wins my friends," whooped Vettel over the radio after taking the checkered flag and giving his trademark finger-in-the-air salute.
"I was very happy with how the race went today, I had the feeling we got everything out of the car," he grinned.
"After last weekend with the drivers' championship and this week the constructors' it's fantastic," said the German, who added a final touch to the celebrations with the fastest race lap right at the end.
Hamilton finished runner-up, 12 seconds behind the sport's youngest double champion, with Australian Mark Webber third for Red Bull and just 0.4 adrift.
The Briton, who had started on pole position for the first time since Canada in June last year, had appeared almost downcast on Saturday but allowed himself a smile on his first podium appearance for six races.
"It was a good weekend for me compared to what has happened in the past so I'm happy," declared Hamilton, who has been a regular in front of the stewards and in the headlines this season for driving controversies.
Jenson Button, the 2009 champion who won in Japan for McLaren, finished fourth after dropping from third to sixth at the start with Ferrari's Fernando Alonso and Felipe Massa fifth and sixth respectively.
After predictions of a flurry of pitstops and heavy tire degradation, the leaders made just two trips to the pits on an afternoon short on thrills at the little-used circuit 320km south of Seoul.
Mercedes's Schumacher retired on lap 17 after his car was speared in the rear by Vitaly Petrov's Renault into turn three. The Russian nursed his car back to the garage and called it a day.
The collision brought out the safety car for three laps while marshals collected the debris from a collision that Alonso narrowly avoided.
Hamilton and Webber then provided the main excitement with a closely fought duel that saw the pair fighting and trading positions repeatedly before and after the second pitstop.
Toro Rosso had Spaniard Jaime Alguersuari and Sebastian Buemi finish seventh and ninth with Mercedes' German Nico Rosberg eighth. Britain's Paul Di Resta took the final point for Force India.
"A second title is testimony to the dedication and commitment of the whole team," said Red Bull team boss Christian Horner, who joined in the podium celebrations.
"We're going to enjoy this moment. It's been a phenomenal period for the team, and I'm tremendously proud of all of them."
