Edwards and Hayden had been the fastest riders on track in the closing stages, before Hayden backed off to confirm a repeat of his 2010 British GP result. Rizla Suzuki's Alvaro Bautista rode to an admirable fifth in his team's home event and was the last rider within one minute of Stoner.
Starting just 13th on the grid, and after a fall in morning warm-up, Valentino Rossi's first Silverstone race ended in a forgettable sixth place, while rookie Karel Abraham turned a MotoGP-best sixth on the grid into seventh at the flag.
Toni Elias (LCR), Hiroshi Aoyama (Gresini) and Loris Capirossi (Pramac) completed the top ten, with Hector Barbera (Aspar) and Randy de Puniet (Pramac) both lapped by Stoner.
With Dani Pedrosa joining home star Crutchlow on the collarbone injury list, only 15 riders began the race.
Silverstone returned to the MotoGP calendar last year and the 2011 event marked the debut of the circuit's new £27-million Pits & Paddock. 72,544 trackside fans watched Sunday's race.
The Dutch TT at Assen takes place on June 25.
Race results - Silverstone:
12. de Puniet