JOIN USAustralian Mark Webber finished runner-up, 15.1 seconds behind the 21-year-old, with Brazilian Rubens Barrichello in third place for Brawn GP.
Britain's Button, winner of six of the first seven races, had his overall lead over Barrichello trimmed to 23 points after finishing off the podium for the first time this year.
The dominant victory, from pole position in a race low on incident, was Vettel's second of the season and third of his Formula One career.
The German, who also led Red Bull to a one-two in China in April, is now 25 points adrift of Button with nine races remaining.
"Thank you very much guys, this is a dream coming true. We've won the British Grand Prix," he said over the team radio after taking the chequered flag.
"This is what I was dreaming of when I saw the first grands prix at Silverstone in the era of (Britain's 1992 world champion Nigel) Mansell," he added later.
Ferrari's Felipe Massa was fourth, ahead of Germany's Nico Rosberg for Williams.
Italy's Jarno Trulli was seventh for Toyota, with Ferrari's Kimi Raikkonen taking the last point in a race billed as a farewell to the track that hosted the first Formula One championship race in 1950.
Red Bull's superiority over the Mercedes-powered Brawn was underlined by Vettel lapping more than a second a lap faster than his rivals in the early stages, despite being heavier on fuel, and finishing 41.1 seconds ahead of Barrichello.
"I don't think we could have beaten them today," said Brawn owner Ross Brawn.
Button, who had struggled all weekend for grip and to get heat into his tyres, started sixth but had fallen to ninth after the opening lap. He worked himself back into the points and then made up two places at his second pitstop, when he switched to softer tyres and chased Rosberg all the way to the finish. McLaren's Lewis Hamilton, who won by a massive 68 seconds in the wet race last year, finished 16th -- the Briton's fourth race in a row out of the points.
Fisichella 10th, Sutil 17th
The new aero package could not inspire Force India to break their points jinx but Giancarlo Fisichella drove a consistent race to finish 10th.
Fisichella’s German teammate Adrian Sutil finished 17th.