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, shock winner in Singapore last week, took third with Kimi Raikkonen fourth in the second Ferrari.
"Awesome stuff, Lewis! Fantasic race, mate!" his Mercedes team engineer said over the radio as Hamilton crossed the line pumping his fists in celebration after his eighth win of the season.
Stung by his Singapore flop, Hamilton got off to a sensational start, darting into the lead at turn two after Rosberg slithered onto the grass and fell to fourth from pole.
Red Bull's Daniel Ricciardo shredded a tyre trying to thread the needle 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, allowing Vettel to boost his slim title chances.
Hamilton survived a scare midway though the 53-lap race, complaining of vibrations and overheating in the cockpit.
"I'm struggling out here," he said, although it proved to be only a temporary glitch as he pulled away to equal boyhood hero's Ayrton Senna's tally of 41 grand prix victories.
Rosberg recovered from his poor start and took second on lap 32 when Vettel pitted but emerged just behind his fellow German.
With Formula One in sombre mood a year after Frenchman Jules Bianchi's fatal crash at Suzuka, there was relief for race organisers when the rain that washed out much of Friday's practice held off over the weekend.
Valtteri Bottas finished fifth for Williams after qualifying third fastest with Nico Hulkenberg sixth for Force India ahead of Romain Grosjean and Pastor Maldonado for the troubled Lotus team.
You’ve reached your limit of {{free_limit}} free articles this month.
Subscribe now for unlimited access.
Already subscribed? Log in
Subscribe to read the full story →
Smart Quarterly
₹900
3 Months
₹300/Month
Smart Essential
₹2,700
1 Year
₹225/Month
Super Saver
₹3,900
2 Years
₹162/Month
Renews automatically, cancel anytime
Here’s what’s included in our digital subscription plans
Exclusive premium stories online
Over 30 premium stories daily, handpicked by our editors


Complimentary Access to The New York Times
News, Games, Cooking, Audio, Wirecutter & The Athletic
Business Standard Epaper
Digital replica of our daily newspaper — with options to read, save, and share


Curated Newsletters
Insights on markets, finance, politics, tech, and more delivered to your inbox
Market Analysis & Investment Insights
In-depth market analysis & insights with access to The Smart Investor


Archives
Repository of articles and publications dating back to 1997
Ad-free Reading
Uninterrupted reading experience with no advertisements


Seamless Access Across All Devices
Access Business Standard across devices — mobile, tablet, or PC, via web or app
