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 on Sunday 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.
He also won the world title in 2008 with McLaren.
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.
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.
Dropped into second, Rosberg couldn't keep up as Hamilton put more time between their cars with every lap.

Hamilton had the more muscular car through the week's practice sessions, only to lose the pole position because of braking problems that dogged his session.
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.

Vettel, the defending race and world champion, started from pit lane after incurring a penalty for using his sixth engine of the season, but fought all the way back to finish seventh.
Vettel is leaving Red Bull at the end of the season, but has yet to confirm where he'll drive in 2015.

The race started with just 18 cars, the smallest field in nearly a decade after financial problems forced teams Marussia and Caterham to drop out.
Saturday's practice and qualifying sessions were dominated by speculation that three more struggling teams, Lotus, Sauber and Sahara Force India, could stage a protest by either boycotting the race or pulling out after one lap, but neither threat materialised.
The race went under safety car on the first lap when Force India's Sergio Perez collided with Sauber's Adrian Sutil, knocking both drivers out of the race. The crash was a major blow for Sauber, which hoped to capitalise on Sutil's first top-10 qualifying position of the season.
Force India then lost its second car when Nico Hulkenberg retired in the 17th lap.

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