Hamilton finished only ninth following the explosive turn-three incident, after which the British driver asked if Vettel had deliberately crashed into him.
The championship rivals both sustained damage in the collision as Hamilton's Mercedes limped back to the pit lane with a right-rear puncture while Vettel stopped for repairs to his Ferrari's broken front wing.
And although a determined Vettel fought back through the field to cross the line in fourth place, he fell well short of the victory he required to prevent Hamilton from winning the title with two rounds to spare.
Max Verstappen, who also banged wheels with Vettel in a frenetic start to Sunday's race, took advantage of the first-lap mayhem to win from Valtteri Bottas with Ferrari's
Kimi Raikkonen completing the podium places.
Hamilton, 32, has now surpassed Sir Jackie Stewart by becoming the first British driver to win more than three titles.
He had vowed to seal his fourth championship in style. After qualifying only third, Hamilton knew that the 800-metre charge to the first corner – the longest on the calendar – represented his best chance of writing his name into the record books with his 10th victory of the year.
Pole-sitter Vettel, Verstappen and Hamilton charged three abreast at 220mph into the left-handed opening turn. Verstappen then made his move around the outside of Vettel at the right-handed second corner before the pair banged wheels.
Vettel then clumsily tapped the back of Verstappen's Red Bull before Hamilton sensed his opportunity. He roared around the outside of Vettel at the ensuing turn, and the Ferrari driver – now down to third – made contact with Hamilton's right-rear rubber.