The 31-year-old Englishman came home 6.9 seconds clear of Mercedes teammate Rosberg.
The world champion delivered a fearless display of front-running to register his third successive Silverstone victory ahead of Rosberg, whose bad day got worse with a 10-second post-race penalty which dropped him to third behind Max Verstappen.
In fact the safety auto was in more danger than Rosberg as Hamilton all but collected it in his anxiety to start racing properly and coming home to the adulation of his overjoyed supporters.
Hamilton celebrated with a "crowd surfing" demonstration of joy.
Speaking to Sky Sports, Hamilton said: "In terms of my race craft, that's always been with me, I'm growing with the vehicle, learning more about the auto, comfortable with myself, that also reflects in my performance".
The altered result cut Rosberg's lead over his teammate Lewis Hamilton, the victor of Sunday's race, from four points to one point in the drivers? championship.
The home crowd were on their feet as Hamilton took the last lap to take the chequered flag by more than six seconds over Rosberg.
The stewards issued a ten-second time penalty, dropping Rosberg behind Max Verstappen, who finished 1.339s behind him on the road.
"It was a cool fight", said Rosberg.
Rosberg crossed the line in second place but after an investigation by race stewards was given a 10-second penalty for contravening radio rules.
Mercedes, who had advised Rosberg to avoid seventh gear because his car's gearbox was failing, said they meant to appeal.
Engineer:: "Avoid seventh gear, Nico, avoid seventh gear".
"But I really feel that since that low after Barcelona [where Hamilton and Rosberg crashed out on the first lap], I was able to cultivate a very positive and strong mental attitude, and that's what I have today".
Rosberg leads Hamilton overall, 168 points to 167, with Raikkonen third at 106.
Head of Mercedes motorsport Toto Wolff argued that the team acted within the rules since it is permitted to advise of critical problems with the vehicle. But the advice to avoid seventh gear was considered a breach of Article 27.1 of the Sporting Regulations, regarding what can and cannot be discussed over team radio.