Vettel started from second on the grid, but within seconds had overtaken Red Bull teammate Mark Webber and was untouchable after that, beating Webber by 30.8 seconds over 55 laps, and finishing 33.6 clear of Mercedes driver Nico Rosberg.
"The car was flawless, it doesn't happen that often that the car responds to everything you want," Vettel said. "I am looking forward to tonight, where there will be a few drinks."
Although the German had already clinched his latest title at the Indian GP last weekend, he proved beyond any doubt that his thirst for victory is unquenchable.
"Obviously, winning is very special," Vettel said. "Seven races in a row - every single one is tough."
Vettel now has 37 career race wins and looked stunned when told he had just matched Schumacher's run of seven wins in a row in one campaign.
"I remember watching Formula One as a kid (when) Michael was dominating for Ferrari," Vettel said.
Vettel can set a single-season record with eight straight at the United States Grand Prix in two weeks' time. Then, victory at the season-ending Brazilian GP a week later will see him match Ascari.
"People see seven races they don't see the challenge it takes every race to nail it," Vettel added. "We got everything right, pit stops, reliability. The numbers aren't that important to me but equally they make me very, very proud."
Moments after winning, Vettel jogged over to his waiting parents.
"I have spent most of my life racing in front of them as a kid," Vettel said. "The cars are a bit bigger now but I am so pleased they are here to see me today."
Just like last weekend, Vettel celebrated the win with a few screeching doughnuts on the Yas Marina circuit. He was fined last time, but is unlikely to care too much.
Webber's last win was at the British GP in July last year and the 37-year-old never looked like making it 10 career wins.
The Australian has never been known for his pure speed and made a poor start, allowing Vettel and then Rosberg to pass him.
"The start wasn't great and Nico got an unbelievable start," Webber said. "I would have liked the win but I matched my best result here. There are plenty of Aussie fans here so thank you."
Overall it was a good day for Mercedes in the battle with Ferrari for second place in the constructors' championship.
"Our aim for the weekend was to be best of the rest," Rosberg said. "I was very happy to hear that we took some more points from them."
Red Bull has already won the constructors' title with 513 points. Mercedes is next with 334 points to Ferrari's 323.
"The most important thing is to finish second in the constructors' championship, not only financially but also motivationally for the team," Rosberg said.
Force India driver Paul di Resta finished sixth ahead of Mercedes driver Lewis Hamilton and Ferrari's Felipe Massa.
Qualifying and the race itself are held at twilight here, allowing the track to cool and the drivers to avoid the stifling daytime heat.
Kimi Raikkonen's day proved even more difficult with the Finn retiring on lap one with suspension damage.
"The Caterham only touched a little bit the front wheel, but the angle was so bad it damaged my suspension," Raikkonen said.
The 2007 world champion threatened not to race at all because Lotus has not paid his wages all year. Then he qualified fifth only to be demoted to the back of the grid after his car failed a post-qualifying inspection because of an illegal floor.
As Vettel pulled away, Webber complained over race radio that his KERS power-boosting system was not working properly, costing him valuable seconds as Grosjean pressured him.
Vettel's lead was so commanding that he could take his first pit stop and still come out comfortably ahead of the chasing pack.
Webber showed some slick driving to go around Rosberg to pull back into second place, but he was still a massive 27 seconds behind Vettel by the midway point.
"Seb was well and truly gone," Webber said.
With 10 laps to go, Alonso went off the track after nearly colliding with Vergne's Toro Rosso. Stewards investigated whether he stayed within the track limits but cleared the Spaniard after the race.
Alonso has not won a race since the Spanish GP in May, but with Raikkonen out he did at least consolidate his second place in the drivers' standings.
However, when Alonso looks at the points - Vettel has 347 to his 217 - he will realize just how badly he was beaten this season, having failed to beat Vettel by just three points last year.
STANDINGS
Sebastian Vettel 347
Fernando Alonso 217
Kimi Raikkonen 183
Lewis Hamilton 175
Mark Webber 166
Nico Rosberg 159
Romain Grosjean 114
Felipe Massa 106
Jenson Button 60
Paul di Resta 48
- AP
