© Reuters
Vettel's third win in a row, fourth of the season and 25th of his career, left him on 215 points with third-placed Alonso now on 209.
Australian Mark Webber, who had started on pole position but was overtaken by his team mate off the grid into the first corner, finished second to anchor the first one-two of the season by any team.
South Korea's 'Gangnam Style' rapper Psy waved the chequered flag as Vettel crossed the finish line and thanked his team for a "great race, great job on the pit wall" before screaming in delight.
"The start was very important. we started from the dirty side," said Vettel. "I had a very good launch and could see that Mark was struggling a little bit. I was able to get side by side and then had the inside into turn one.
"It was a perfect start for myself," added the German, who spent the closing laps fretting about the tyres and making sure they held up.
With no need to attack his title-chasing team mate in the closing stages, Webber finished 8.2 seconds behind Vettel.
Starting fourth, Spaniard Alonso got ahead of McLaren's Lewis Hamilton at the start but could not close the gap with the Red Bulls on an afternoon where the outcome was effectively decided in the first few seconds. He crossed the line 13.9 seconds behind Vettel.
"I think we have to be happy with the performance today," said Alonso, whose Ferrari team (290 points) overtook McLaren (284) for second place in the constructors' standings behind Red Bull (367).
"We are moving in the right direction. We just need a little last step to be as competitive as Red Bull."
BUTTON OUT
Brazilian Felipe Massa continued his late season resurgence with fourth for Ferrari.
Kimi Raikkonen chalked up his 13th successive points finish with fifth in the race for Lotus to consolidate third place overall and stay in the reckoning.
McLaren's Jenson Button was an early casualty, his race ending on the first lap when Sauber's Kamui Kobayashi sideswiped his car and smashed the front right suspension as well as puncturing the tyre.
Kobayashi, who also ended the race for Mercedes' Nico Rosberg in the same incident, made it back to the pits on three wheels and a rim.
The Japanese, who finished a memorable third at home last weekend, collected a drive-through penalty for causing the collision and retired in the pits on lap 18.
Button, now 84 points off Vettel, declared his remote title hopes to be defunct.
"No, definitely not," said the Briton when asked whether he could still win the championship. "I'm going to enjoy myself over the next few races. Points for the team would have been really important, but it's out of our hands."
Germany's Nico Hulkenberg was sixth for Force India with Frenchman Romain Grosjean, steering well clear of trouble after a spate of first lap smashes, seventh for Lotus.
Frenchman Jean-Eric Vergne was eighth for Toro Rosso, with Australian team mate Daniel Ricciardo ninth.
Hamilton, who had a ripped off strip of astroturf trailing from a sidepod in the closing laps, just kept off Sauber's Mexican Sergio Perez - the man who replaces him at McLaren next season - for 10th place after starting third.