With four races to go starting in India in two weeks, Vettel, the reigning champion who is chasing a third drivers' title in a row, sits atop the standings with 215 points. Alonso, who finished third, is on 209.
It was the 25-year-old German's third win in three races and he will now be favourite to retain his crown, in what had been a highly unpredictable season until he took the championship by the scruff of the neck.
Second at a cool but sunny Yeongam was Vettel's teammate Mark Webber, who started on pole. It was the first Red Bull one-two of the season.
Alonso's fellow Ferrari driver Felipe Massa, second at Suzuka seven days ago, continued his resurgence with a fourth-placed finish. Lewis Hamilton, who still had title aspirations going in this grand prix, finished 10th.
Fifth was Kimi Raikkonen of Lotus, followed by Nico Hulkenberg in a Force India. Romain Grosjean (Lotus), Jean-Eric Vergne, Daniel Ricciardo (both Toro Rosso) and Hamilton rounded out the top 10.
"Very pleased. Fantastic, I'm very happy," Vettel told the crowd, having celebrated his 25th career victory by jumping on top of his Red Bull with his arms aloft. "It was a fantastic race.
"Towards the end I felt I had a bit more in the tyres," said Vettel, whose front-right tyre in particular was badly worn by the end. He had been warned repeatedly by his team to "look after" his tyres.
"I could've gone on a bit longer. We were all a bit worried about the front tyres."
Alonso, also a double world champion, put a brave face on losing his lead in the standings. "We have to be happy with the performance today," he said. "It was a good day for the team and for me. Today was better than expected."
Vettel, who started second on the grid behind Webber, nipped in front of his teammate at the first corner. Behind them Alonso and Hamilton duelled over third place, with the Spaniard winning through.
Jenson Button's bad weekend finished almost as soon as the race began. His fine start from lowly 11th was wrecked when Kamui Kobayashi came flying down the inside, smashing into Button and destroying his suspension.
"I've just been hit by Kobayashi. What an idiot!" the McLaren driver and 2009 world champion exclaimed over the team radio.
Also out, not long afterwards, was Nico Rosberg, who retired his Mercedes because of the same incident. The Sauber driver Kobayashi, third last week in his native Japan, was forced to pit for a new nose and tyre.
He was then landed with a drive-through penalty for causing the early carnage, and bowed out soon afterwards when Sauber decided that the damage to his car was too extensive.
The Sauber team tweeted before the race was out: "Kamui says with 4 cars side by side after the start he had nowhere to go but to brake at some point. He is very sorry for Jenson and Nico!"
Vettel, the man in form after victories at the last two races in Singapore and then Japan last week, was in firm command. Webber — intentionally or not — was a buffer between the leader and the chasing pack.
The Red Bull duo were exchanging fastest laps in front of a good crowd — the last two races at Yeongam have failed to attract spectators — while an improving Massa shoved a struggling Hamilton further down the field.
Vettel had a shaky moment on lap 35 of 55 when he ran wide, before pitting to go onto softer tyres. Those tyres were wearing out fast by the end of the race.
"Sorry to go on here… you won't know when it's too late," his team told him, as he carefully closed out another imperious win. – AFP