The Briton's dashing victory was overshadowed when Frenchman Jules Bianchi was rushed to the hospital, unconscious, after a crash which brought the rain-hit race to a premature halt.
Hamilton ducked superbly inside fierce rival Rosberg on the 29th lap and stormed away to win at Suzuka for the first time and increase his advantage over the German to 10 points with four rounds left this season. Reigning world champion Sebastian Vettel finished third for Red Bull.
"What a day," Hamilton told reporters. "I had a lot more pace than Rosberg and it's not a very easy circuit to follow on but fortunately I was able to get quite close, particularly in the last corner. I was confident with the balance of the car and stuck it out.
"After that I was attacking, attacking and then I could take different lines and manage it differently. Obviously it didn't finish the way I would have hoped and my prayers are with Bianchi and his family."
Typhoon rains had been forecast for yesterday’s race and it began behind the safety car but the drivers were called back to the pits minutes later.
The safety car came out again after 44 laps following Bianchi's shunt and the race was suspended two laps later with the rain getting heavier and the light rapidly deteriorating.
Celebrations were muted on the podium with news already having filtered through of Bianchi's crash.
The early halt came as little surprise after German Adrian Sutil smashed his Sauber into a wall; Bianchi's Marussia was then involved in a collision with a recovery vehicle at the same spot, prompting the safety and medical cars to appear and the race to be stopped seven laps earlier.
Sutil witnessed Bianchi's crash at close quarters after sliding out in similar fashion.
"I had aquaplaning at that corner," he said. "The rain got worse and worse, the visibility got less and less. One lap later, Bianchi came around and had the same spin there, and that was it. It was more or less the same crash, but the outcome was different."
Hamilton, the 2008 world champion, produced one of the overtaking moves of the season when he daringly passed Rosberg on the outside of turn one and stormed away to claim his eighth victory of 2014 and the 30th victory of his career.
"All in all, Hamilton did a better job today [Sunday] and deserves to win," said Rosberg, who struggled with over-steer throughout the race. "Second place is damage limitation for me. Taking everything into consideration — tricky conditions, seven points lost to Hamilton, there is worse than that."
On Bianchi’s crash he told BBC: “I've been given some information and it seems very, very serious. I'm hoping for the best."
Vettel, the four-time defending title holder, who announced on Saturday that he will leave Red Bull at the end of the season, made the podium for the second race in a row – but only his fourth of the year – ahead of Australian teammate Daniel Ricciardo.
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