Rosberg, who started from pole, was forced to retire with a throttle problem, leaving the way clear for Hamilton to claim his ninth win of the season.
Sebastian Vettel finished second for Ferrari and he is now Hamilton's closest challenger in the standings, but 66 points adrift with a maximum 100 on offer in the four remaining races. Rosberg is a further seven points behind.
Sergio Perez took third for Force India after a late incident wrecked the chances of Finland's Valtteri Bottas to claim the final podium place, having overtaken the Mexican on the last lap.
He then went off under challenge from Vettel's teammate Kimi Raikkonen, who race officials later judged to have been at fault in the overtaking move.
The former world champion was given a 30-second penalty, relegating him from fifth to eight place. The loss of points for Ferrari meant Mercedes have clinched a second straight constructors' crown.
Two-time champion Fernando Alonso was also penalized five seconds for exceeding the pit-lane speed limit, moving him out of the points by dropping from 10th to 11th in his McLaren.
If Hamilton's victory was a case of deja vu, the same could be said for the fate which befell Spain's Carlos Sainz Jr.
Bravely racing after his high-speed crash during Saturday's practice left him in hospital, Sainz was in the points until coming off and ending in the same barrier at Turn 13 as the day before, but this time at a lesser speed.
Rosberg had led up off the grid until a safety car was deployed following a coming together between Nico Hulkenberg and Marcus Ericsson at the start.
Rosberg reported to his team that the pedal operating the throttle was broken and after being overtaken by his teammate Hamilton when the race proper got underway again, he had no option but to retire.
There was a second safety car when Romain Grosjean went off in his Lotus at Turn 3 on lap 13.
His car was badly damaged, but fortunately the Frenchman walked away with just a few bumps and bruises.
Hamilton, claiming his second straight win after his non-scoring hiccup in Singapore, has moved ahead of his hero Ayrton Senna with his 42nd career win and within touching distance of a third world title to follow the success of his all-conquering team.