The result left the seven-time champion level on 369.5 points with title rival Max Verstappen ahead of the final race in Abu Dhabi next weekend.
Hamilton was behind Verstappen for much of the 50-lap race which was stopped twice because of crashes and interrupted numerous times by the safety car and virtual safety car.
But Hamilton, nursing a damaged front wing caused by a collision with Verstappen, came through late, to claim his eighth win of the season and the 103rd of his career.
The title will be settled in Abu Dhabi, although if neither finishes in the points it will be Verstappen, who has nine victories, who will take the title.
"I have been racing a long time but that was incredibly tough," said Hamilton who gained an extra point for the fastest lap.
Verstappen finished second, 11.825secs behind in spite of being given a five-second penalty after colliding with the Mercedes star.
He was later sanctioned by 10 seconds by the stewards although that did not impact his finishing position.
"Just trying to race and this sport is more about penalties than racing," said Verstappen.
"For me this is not Formula 1, but at least the fans enjoyed it and I gave it all today, but clearly not quick enough."
Hamilton's teammate Valtteri Bottas pipped Alpine's Esteban Ocon on the line for third place to give Mercedes a 28-point lead in the constructors' championship.
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