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.
Just a week after Jules Bianchi's life-threatening accident in the storm-hit Japanese Grand Prix, where the French driver suffered severe head injuries, the race was preceded by tributes to support his fight for life in hospital in Yokkaichi.
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.
Australian Daniel Ricciardo was seventh for Red Bull ahead of departing German team-mate and four-time champion Sebastian Vettel and Finn Kimi Raikkonen, in the second Ferrari. Mexican Sergio Perez was 10th for Sauber.
"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.
"Sorry, guys," said Rosberg. "That was very unnecessary (his attack on lap one), but thank you for the unbelievable car that allowed me to fight back to take second."
On a hazy, warm day under blue skies and air temperatures of 22 degrees, the race was preceded by ceremonies dedicated to support for Bianchi, around an on-track message that declared 'Jules we are all supporting you'.
The tributes were emotional and palpable and many drivers appeared to be moved before they returned to their teams for the start.
At the off, Hamilton steered diagonally to his right to lead Rosberg towards Turn One, a mild kink en route to Turn Two where the German locked up under braking, as he passed inside Hamilton and ran wide across the run-off area.
For Rosberg, it was an expensive rush of blood. His journey across the brightly-coloured escape zone lifted him into the lead only briefly before his race engineer asked him to 'give position back to Lewis, please.'
Rosberg did so, falling to second before pitting immediately to replace his flat-spotted tyres and re-joining at the back of the field.
Rosberg was soon finding his rhythm, rising to 16th by lap eight, and the top 10 soon after, encouraged by his engineer's message that he was fast enough to finish on the podium. By lap 24, he was seventh and Hamilton held a 12.6sec lead ahead of Bottas.
Button pitted on lap 23, conceding third to Alonso who was 26 seconds adrift. Two laps later Bottas pitted before Alonso came in for a bungled Ferrari stop that saw his car twice dropped early by the front jack man.
All this left Alonso down in ninth behind Massa, who had driven magnificently from the back for Williams. Rosberg rose again to fifth on lap 26 and then, with a forceful move on Bottas, to second on lap 31, when Vettel had pitted.
For the Russian crowd, unfortunately, home favourite Daniil Kvyat was unable to shine as he slipped from his best grid position of fifth down to 14th in his Toro Rosso while the Anglo-Russian Marussia team's sole entrant Briton Max Chilton was forced to retire due to vibrations.
"It's been a very, very difficult week for the team and everyone in the F1 family," he said. "It was hard on the grid and all the drivers were struggling, but hopefully they are putting on a good show for Jules. It's just a shame we couldn't complete the race for him."