Hamilton, who recorded his second triumph in seven days following his masterclass in the United States, is now 19 points adrift of Rosberg with just two races remaining.
The championship battle remains out of the Briton’s control, however, after Rosberg survived a lunge from Red Bull’s Max Verstappen to cross the line in second place.
Indeed Rosberg will now secure his maiden title if he wins the Brazilian Grand Prix in a fortnight’s time. The German can even afford to finish second and third at the remaining two races to clinch the crown.
Verstappen finished third ahead of Ferrari driver Sebastian Vettel, but the former was given a five-second elapsed penalty for leaving the track at turn one and refusing to give the place to Vettel. The German was subsequently bumped up to third.
Hamilton, 31, revealed earlier this week that he is relishing the challenge of usurping his Mercedes team-mate Rosberg at the top of the championship standings.
And the Briton has been in inspired form from the get-go here, comfortably faster than Rosberg in practice and qualifying before claiming the 51st victory of his career with a dominant display in front of 135,000 fans on Sunday.
Hamilton’s season has been plagued by engine troubles and slow starts but, for the second race in succession, the triple world champion got the perfect getaway to retain the lead on the near 1,000-metre run down to turn one.
But perhaps preoccupied with keeping Rosberg behind, Hamilton locked his front-right tyre and ran on to the grass. He essentially missed out the opening four turns before rejoining the track but, as Rosberg and Verstappen banged wheels behind him – a coming together which was declared a racing incident following an investigation by the stewards – he remained in the lead. Despite being bumped on to the grass, Rosberg retained second ahead of Verstappen.
Esteban Gutierrez, Marcus Ericsson and Pascal Wehrlein then tripped over one another with the latter sustaining significant damage to the front of his Manor. His race was over, and the safety car was deployed with debris scattered across the track.
When the race restarted on lap four, Rosberg failed to threaten Hamilton, and from there the show was all but over. Vettel, on a longer first stint, led for 12 laps but, after he pitted at the end of lap 32, and Hamilton was released back into the lead, it was only a matter of the world champion nursing his Mercedes home, which he did to fine effect.
Hamilton took the chequered flag a distant eight seconds ahead of Rosberg to move alongside four-time world champion Alain Prost, into second on the all-time winners’ list. Only Michael Schumacher has tasted more victories in Formula One’s long history than the man from Stevenage.
For Rosberg, second could yet be enough as he bids to emulate his father Keke, the 1982 world champion, and win the title. In a race of little drama, Verstappen attempted to pass Rosberg on lap 50 after the German came unstuck while lapping Carlos Sainz, but Verstappen failed to make his move stick.
There was controversy late on, too, after Verstappen was stripped of his podium place following a timed penalty which promoted Vettel to third and Daniel Ricciardo to fourth.
Verstappen, who only discovered he had been penalised as he prepared to step on to the podium, was adjudged to have left the track and gained an advantage.
Jenson Button, the 2009 world champion, crossed the line in 12th with British rookie Jolyon Palmer 14th.