The Briton, who is chasing back-to-back Formula One championships, opened a 48-point gap over Rosberg with five races left after putting on a masterclass at Suzuka.
Sebastian Vettel, surprise winner in Singapore last week, took third with Kimi Raikkonen fourth in the second Ferrari.
“Awesome stuff, Lewis! Fantastic race, mate!” Hamilton’s team engineer said over the radio as he took the chequered flag 19 seconds ahead of Rosberg, pumping his fists to celebrate an eighth victory in 14 races this season.
After hitting back in style from his first race-ending retirement in over a year in Singapore, Hamilton whooped: “Fantastic job, guys. So great to be back up here.”
Dripping with champagne, Hamilton added: “It was important for us to strike back. We didn’t bring our A-game in the last race. We had to make sure we brought it here.”
Stung by last week’s flop, Hamilton got off to a flying start, darting into the lead at turn two after Rosberg slithered onto the grass and fell from pole to fourth.
Red Bull’s Daniel Ricciardo shredded a tyre trying to thread the needle in the dash for the first corner and brushed wheels with Felipe Massa, whose Williams also had to limp back to the pits for a change of front wing.
Normal service was resumed at the front of the pack, meanwhile, after Mercedes were rocked by a mysterious loss of pace in Singapore, which allowed Vettel to boost his slim title chances.
Their mojo firing again in brilliant sunshine in Japan, the two Mercedes destroyed the Ferraris with Hamilton relentlessly pounding out fastest lap after fastest lap.
He survived a scare midway though the 53-lap race, complaining of vibrations and overheating in the cockpit but it proved only a temporary glitch as he pulled away to equal boyhood hero’s Ayrton Senna’s tally of 41 victories.