Lewis Hamilton dominated the German Grand Prix to move into a 19-point lead in the championship over Mercedes team-mate Nico Rosberg.
Hamilton shot into the lead at the start from second on the grid as Rosberg slipped to fourth, where he finished after a difficult afternoon.
Rosberg was penalised for forcing Red Bull's Max Verstappen off the track.
The German finished behind Red Bull's Daniel Ricciardo and Verstappen after being unable to make up the lost time.
It was the icing on the cake for a perfect afternoon for Hamilton, who has put a stranglehold on the championship after a remarkable recovery from a difficult start to the season.
As Hamilton drove away and Rosberg was swamped, Verstappen overtook team-mate Daniel Ricciardo brilliantly around the outside
In seven races, Hamilton has turned his season around, moving from a 43-point deficit to Rosberg after five races to his current advantage of just six points short of a entire win.
Hamilton knows he will have to take a grid penalty for using more than the permitted number of engine parts at one of the first two races after the summer break, starting with the Belgian Grand Prix at the end of August.
And he targeted a result like this to try to ensure that when he does have to start from the back, he will not leave that race with another big deficit to Rosberg.
Hamilton joins the greats as three-time German GP winners: Ayrton Senna, Jackie Stewart, Juan Manuel Fangio and Fernando Alonso. Source: Forix
This victory was determined by the start. Rosberg, who had taken a superb pole position under highly pressured circumstances on Saturday, bogged down off the line.
Hamilton shot into the lead, and Rosberg exited the first corner behind both Red Bulls as well, with Verstappen slotting into second ahead of Ricciardo.
Despite the Mercedes' inherent pace advantage, Rosberg was unable to pass either Red Bull before the second pit stops just before the 30-lap mark.
The key moment for Rosberg's attempt to recover ground on Hamilton came after that stop.
Verstappen was overtaken by Rosberg for second place, but Rosberg was penalised for being too aggressive
Mercedes tried the 'under-cut' on Verstappen, getting an advantage by stopping a lap earlier, and when the Red Bull emerged from its stop at the start of lap 29, Rosberg was right behind Verstappen.
Rosberg dived late for the inside into Turn Six, as Verstappen moved to the right to defend in the braking zone - a manoeuvre which he has made something of a trademark, to the anger of the other drivers, who feel it breaks a gentleman's agreement between them about a dangerous tactic.
In response, Rosberg went straight on deep into the corner, and emerged ahead.
But Verstappen complained on the radio he had been "forced off the track", the stewards looked into it and penalised Rosberg five seconds.
Rosberg, who passed Ricciardo into second when the Australian made his second stop on lap 33, had to serve that at his third and final pit stop on lap 44, dropping back to fourth again.
He emerged 5.4 seconds behind Verstappen but could make no progress towards the Red Bulls and had to settle for a disappointing fourth.
Rosberg now has a four-week break to ponder how his season has fallen apart, and his best chance yet of winning the title appears to have already as good as evaporated.
"No, I don't have Lewis one." Rosberg was driving at his home grand prix
Ferrari had an underwhelming first race following the departure of technical director James Allison, with Sebastian Vettel and Kimi Raikkonen an anonymous fifth and sixth, ahead of the Force India of Kimi Raikkonen.
Behind Force India's Nico Hulkenberg, McLaren's Jenson Button passed Williams' Valtteri Bottas for eighth place on the penutimate lap, just after team-mate Fernando Alonso had lost out to Force India's Sergio Perez for the final point after a mix-up with Verstappen as the Red Bull lapped the McLaren and then slowed down.
Alonso backed out of an attempt to unlap himself, and Perez took advantage of the McLaren's wearing tyres to slip by after Alonso locked up on the entry to Turn Six.
It's Michael Schumacher who has the most German GP wins, with four. Source: Forix
Mick Schumacher, the son of seven-time F1 champion Michael, watched the German GP weekend from the pit garages
X-man: Actor Nicholas Hoult was on the grid