The victory put a smile on the Australian's face after having to give his car's front wing to the German on Saturday in a controversy that left Red Bull facing accusations of favouritism.
Webber, stony-faced on Saturday, let his feelings pour out as he crossed the line, telling the team over the radio: "Fantastic, not bad for a number two driver".
"Well done Mark, you can smile now," replied team boss Christian Horner.
Vettel, who had started on pole only to find himself at the back of the field after the first lap, fought back to finish seventh.
Britain's Lewis Hamilton [ Images ] delighted the 120,000-strong crowd with a fighting second place for McLaren [ Images ], 1.3 seconds behind Webber, to extend his championship lead over team mate Jenson Button [ Images ] to 12 points with nine races remaining.
World champion Button, starting 14th after describing his car as 'undriveable' on Saturday, carved his way through the field to finish fourth on a bright afternoon at the new Silverstone circuit.
While a remarkable drive in the circumstances, Button still found himself off his home podium for the 11th season in succession.
The story of the race was the start, with the two Red Bull drivers lining up alongside each other on the front row with the battle lines drawn.
Webber, more than ever the Australian hard man, gave no quarter and forced Vettel wide on to the rumble strips while avoiding a repeat of the collision in Turkey that wrecked Red Bull's hopes of a one-two.
The one-two still evaporated in the haze of exhaust fumes, Vettel having to pit at the end of the opening lap with a punctured right rear tyre after a glancing blow from Hamilton's McLaren.
The 23-year-old, last year's winner from pole in Britain, could still hold his head high after staging a thrilling fightback that included scything past compatriot and seven-times champion Michael Schumacher [ Images ].