Mercedes started the race on pole with Lewis Hamilton, but it was his teammate Nico Rosberg who took victory at Silverstone.
Hamilton, along with three other drivers, suffered identical tyre punctures, placing official tyre supplier Pirelli under massive scrutiny.
Hamilton made an excellent start, leading the pack away as Vettel overtook Rosberg into the first corner.
Webber had a dreadful first lap, falling back to 15th after being squeezed off the track and later came through on the radio to ask, "What the hell happened on that start?"
Hamilton began to pull away and settle into a smooth race pace in the early stages, creating a healthy gap with Vettel in second.
On lap eight Hamilton was seen slowing after his left-rear tyre punctured, simultaneously breaking the hearts of the 125,000 home crowd.
Coming onto the Wellington Straight, Hamilton was seen weaving slightly to regain control. A slow crawl back to the pits for new tyres saw him back out in last place.
Further punctures came soon after with Massa spinning off at the Loop on lap 10 and Vergne on lap 15, both on the same left-rear wheel that affected Hamilton.
Debris sprawled across the track brought out the safety car.
The safety car circled for six laps whilst the marshals swept the debris clear from the racetrack.
Drivers were warned to stay away from the kerbs when their tyres are running hot. When Vettel pitted, there were cuts visibly seen in his tyres.
There was an air of tension in the pitlane, with Pirelli personnel asked whether it was safe to go racing.
Pirelli obtained the punctured tyres and the investigation started in earnest.
On the restart, Hamilton was up to 14th and drivers quickly settled back into a steady race pace.
With the pack close together, there were battles throughout the field and some excellent driving between Alonso on Raikkonen and Hamilton on Di Resta.
With 12 laps remaining, Vettel was looking strong for a victory, but coming out of the last corner his gearbox expired and he crawled to a halt.
The Silverstone crowd were jubilant in their response, clearly delighted with the sight of the World Champion retiring for the first time in 2013.
The safety car made a second appearance to remove the stricken Red Bull, closing the pack up again. Gearing up for a thrilling final shootout for the win, Rosberg led Raikkonen Sutil and Webber.
The final 5 laps were thrilling with some great overtaking moves across the field.
But it was Rosberg who maintained his composure to secure his second win of the season and third overall of his career.
Mark Webber, racing in his last British Grand Prix following the announcement of his retirement from F1 at the end of this year, finished in 2nd place with Fernando Alonso coming home in 3rd to complete the podium.
British fans will be left disappointed, despite a sterling comeback by Lewis who finished in 4th place at the chequered flag.
Paul Di Resta came home in 9th, Jenson Button down in 13th and Max Chilton finishing in 17th.
Focus will now switch to Pirelli to find a quick solution to the tyre punctures seen at this race and through the season to date. With the next race just one week away in Germany it is unlikely any changes will be made to the structure of the tyres before then.
Drivers were asked after the race about racing when they knew there were tyre punctures happening.
"It's not good," said Finnish driver Valteri Bottas of WIlliamsF1.
Lewis Hamilton was asked about Mercedes' involvement in the recent test held by Pirelli using Mercedes cars.
"I'm going to have to bite my tongue on that one and not answer," he said.
It is a problem for Formula One to fix, and it will need to do so quickly.
As for the championship, Vettel not scoring at Silverstone has helped Alonso to close the gap to 21 points.
Rosberg's win also puts him to within 7 points of his teammate Lewis Hamilton who is in 4th.