The 23-year-old German led from his 19th career pole position to the chequered flag unchallenged, conceding the lead only once during his pit-stops, as he claimed his third win in four races this year.
It was the 13th win of his career and another day of celebration for the Red Bull team as Vettel's team-mate Australian Mark Webber overtook in a brilliant manoeuvre in the closing stages two-times champion Spaniard Fernando Alonso of Ferrari to finish second.
It was the England-based team's first one-two of the season and came at the conclusion of an action-packed contest full of overtaking moves and incidents.
Alonso, revelling in a much-improved Ferrari, finished third ahead of Briton Lewis Hamilton, the 2008 champion, who came home fourth for McLaren after a typically roller-coaster afternoon including one pit stop wrecked by a sticky wheel nut.
For Alonso, and Ferrari, it was their first podium finish of the season and confirmed they are back among the contenders after a tricky start to the year.
German Nico Rosberg was fifth for Mercedes ahead of Briton Jenson Button in the second McLaren, the 2009 champion losing ground after planning a three-stop race while most of his rivals went for four.
Another German Nick Heidfeld finished seventh for Renault ahead of Russian Vitaly Petrov in the second Renault, Swiss Sebastien Buemi of Toro Rosso, and the dazzling Japanese driver Kamui Kobayashi of Sauber, who finished 10th after starting at the back of the grid.
Germany's seven-times champion Michael Schumacher, 42, finished a disappointing 12th for Mercedes, one place behind Ferrari's Brazilian Felipe Massa, his former team-mate.
The race featured a total of 73 pit stops - the most since the 1993 British Grand Prix at Donington, run in torrential rain and won by the legendary late Brazilian Ayrton Senna for McLaren.
Vettel's winning time was one hour 30 minutes and 17.558 seconds."Yes," he screamed over his radio at the end. "Yes! That's what I am talking about. What a race. We controlled it from the beginning to the end. Thank-you."
Red Bull team boss Christian Horner was delighted, thanking his drivers for their pace and discipline 12 months on from their acrimonious clash in last year's race.
He said: "It is a sweet victory today; excellent from the drivers, fantastic pit stops, great strategy and a great race."The race was run in perfect conditions, dry and warm under a clear blue sky with most of the decisive action coming in the opening laps.
At the start, Vettel swept clear of the field to establish his supremacy while behind him Rosberg also enjoyed a faultless getaway off the grid that took him up to second ahead of Webber.
The Australian, like most of the men starting from the 'dirty' outside of the grid, was unable to resist Rosberg's surge while Hamilton, after an initial bold assault to gain places, over-played his efforts and dropped back to sixth behind Alonso and Button.
All of this frantic action left Vettel in control after the opening laps ahead of the pack while Massa fought his way up to seventh for Ferrari. Schumacher was involved in a collision with Petrov's Renault, the German turning in and touching the Renault's rear wheels.
This resulted in a pit-stop for a new front wing for Schumacher who fell to the back of the field while Hamilton and Button, the McLaren team-mates, fought for fifth place.
Their battle saw the 2008 champion surge past the 2009 champion on lap seven only to see their positions reversed a lap later, Hamilton having worn his tyres severely.
Kobayashi, who had started at the back in his Sauber, also made rapid progress and had climbed to fifth by lap 12 on one set of tyres as everyone else fought wildly - the two Renault men were even seen shaking their fists at each other.
Vettel, though, was untroubled by all these going on and drove seamlessly on to extend his lead in the overall standings.
