The 29-year-old Briton, starting from his 38th pole position, cruised to the 31st success of his career to draw level with fellow-Englishman Nigel Mansell in the record books, finishing the race 13.657 seconds ahead of Mercedes team-mate and nearest rival German Nico Rosberg.
Hamilton's win lifted him 17 points clear of Rosberg, who made a mistake on the opening lap and, after a pit stop, recovered from the back of the field. Hamilton now has 291 points to Rosberg's 274 with three races remaining.
Hamilton's win was his ninth this year and the result delivered Mercedes' ninth one-two of the season as they ended Red Bull's four-year dominance of the teams' crown. They will now aim to beat McLaren's record of 10 wins set in 1988.
Finn Valtteri Bottas finished third for Williams ahead of Briton Jenson Button and his McLaren team-mate, Danish rookie Kevin Magnussen, with two-time champion Fernando Alonso of Spain finishing sixth for Ferrari after an inspired, but troubled, drive.
"Congratulations to the team on the constructors' championship -- history in the making," said Hamilton afterwards on team radio before he and the other leading finishers met Russian President Vladimir Putin, who arrived at the circuit with 14 laps remaining to preside over the podium ceremony.