The Briton, fifth on the grid with Vettel lining up on pole position, cashed in on both the Ferraris and Red Bull's Max Verstappen smashing into each other within seconds of the start on a wet track.
The victory was the 60th of Hamilton's career — third in Singapore and seventh in 14 races this season — and took him a huge stride closer to a fourth world title with six rounds remaining.
It was also his third in a row after wins in Belgium and Italy and Hamilton set a lap record on his way to the chequered flag.
Australian Daniel Ricciardo finished second for Red Bull, for the third year in a row, with Hamilton's Finnish team mate Valtteri Bottas the final man on the podium.
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