Hamilton - previously champion in 2008 - made the perfect start to grab the lead from polesitting team mate Nico Rosberg, giving him the platform to control the race from the front. Williams' Felipe Massa meanwhile slotted into third from the start ahead of McLaren's Jenson Button, while Valtteri Bottas in the second Williams tumbled down the order after an awful start from third.
For the first 23 laps Rosberg kept Hamilton honest, the duo rarely separated by more than two seconds, but the race turned dramatically on Lap 24 as Rosberg's car began to slow as he lost ERS and then other systems began to fail.
The German began to slip back, the loss of second to Massa the first act of a slow and anguished plummet down the points places. While he did his best to hang on to a top-five result - crucial for his title chances - he gradually slipped out of contention. To add insult to brutal, cruel luck, he was lapped by Hamilton in the closing stages, and eventually finished 14th after Romain Grosjean crept by the stricken Silver Arrow in his Lotus.
Despite such misfortune, Rosberg showed dignity in defeat as he was one of the first to congratulate his season-long championship rival Hamilton. The Briton described his second title - and the first for Mercedes since Juan Manuel Fangio in 1955 - as the greatest day of his life.
But even with Rosberg out of the picture, the Briton's 11th victory of the year was no easy run. Massa was hungry for Williams' first success since Barcelona 2012 and made the best use of a very long second stint to gamble on a set of supersoft tyres for the final 12 laps. Initially he slashed the gap to race leader Hamilton, but with a handful of laps to go his tyres began to lose their vital grip and he didn't quite have enough to challenge the Mercedes, finishing 2.5 seconds behind at the chequered flag.
Bottas did recover from his poor start to clinch third, sealing an excellent day for Williams - it was their first double podium since 2005, and earned them third place in the 2014 constructors' championship.
Daniel Ricciardo drove a brilliant race for Red Bull to surge from the pit lane to fourth, chasing hard after Bottas in the closing stages, while Button drove another blinder to take fifth for McLaren ahead of Nico Hulkenberg's Force India. That was enough to keep McLaren in fifth place overall in the constructors' standings, even though Sergio Perez gave Force India a strong finale by fending off Red Bull's Sebastian Vettel - who like Ricciardo started from the pit lane - in a fight for seventh.
Ferrari had an appalling race, as even Fernando Alonso could only muster ninth on his final drive with the prancing horse, just ahead of team mate Kimi Raikkonen.
Kevin Magnussen was 11th in the second McLaren after first-lap brushes with Hulkenberg and Sauber's Adrian Sutil, while Jean-Eric Vergne was Toro Rosso's sole finisher in 12th after Daniil Kvyat was forced to stop early on with technical problems.
With Grosjean leading the bitterly disappointed Rosberg home, Esteban Gutierrez headed team mate Sutil as their Sauber careers came to an end. It is the first time in Sauber's F1 history that the team have failed to score a point over a season.
Will Stevens was the final finisher for Caterham after a steady debut, as team mate Kamui Kobayashi joined Kvyat and Pastor Maldonado, whose Lotus caught fire, on the retirements list.
"2007 was a very bad experience losing the world championship in the last race," Hamilton admitted. "I fell to a low over which I had no control. In 2008 I came back and won the championship but Felipe here won the race and won the championship for a few seconds, before I got it back in the last corner. So I lost it and won it and, while that was great, my emotions were shot. I wasn't so mature, I didn't have the knowledge I have now.
"Normally before a race you have butterflies in your stomach and are nervous, but today I felt extremely calm. It was weird; was that a good thing or a bad thing? Obviously it was good!
"Last night I kept thinking that tomorrow is the big date, something could happen to the car and that would be the championship done. Naturally you think of all the negative things that could happen but I tried really hard bring all the positives into it, and I brought into the race and looked after the car. It helped when Nico's car was not performing, and when he fell out of the points I knew I could fight Felipe.
"Today was the greatest race of my life."