Hamilton leads Rosberg by 24 points with two races left in Brazil and Abu Dhabi. The final race will be worth double points under a rule change this season.
Red Bull's Daniel Ricciardo was third yesterday for his eighth podium finish on the season.
Rosberg started on the pole, but couldn't hold off Hamilton for even half the race. Hamilton's 10th victory of the season also was the 32nd of his career, passing Nigel Mansell for the most Formula One wins by a British driver.
Hamilton and Rosberg have waged a season-long duel for the title, a tense back-and-forth that has strained their long friendship. Hamilton has won five races in a row, but Rosberg had stayed close in the season standings by finishing no lower than second 10 times.
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Hamilton chased Rosberg for 23 laps, steadily keeping up the pressure and slowing gaining on him. Hamilton finally made his move on lap 24, squeezing inside Rosberg's left on the tight 12th turn out of the long straightaway.
It was the same spot and a similar move to Hamilton's pass of Red Bull's Sebastian Vettel that propelled him to the victory here in 2012.
Given the lead, Hamilton quickly built a gap of more than 2.5 seconds. Rosberg tried to claw back but didn't have enough race left to do it. By the final laps, the biggest challenge for Hamilton was not getting caught up or wrecked by other drivers battling for final position.