Sebastian Vettel of Ferrari took third place, with his team-mate Kimi Raikkonen just behind him.
After the tragedy of last year's race in the rain, when Jules Bianchi's car hit a crane by the side of the track, the 2015 edition was largely uneventful after an exciting start. Felipe Massa and Daniel Ricciardo clashed wheels on the grid but both managed to make it round the track and pit.
Japanese Grand Prix
Hamilton dominates Japanese GP
Only Felipe Nasr retired during the race, and that came two laps from the chequered flag.
Jenson Button was the most vocally disappointed McLaren driver last week in Singapore, and it was Fernando Alonso's turn this time round, declaring loudly that he was embarrassed to be driving a car with what he described as a "GP2 engine".
The win was the Briton's eighth of the season, with Rosberg anchoring the eighth one-two finish for dominant Mercedes as the champions returned to form after a mysterious dip in Singapore last weekend.
Rosberg took the chequered flag 18.9 seconds behind Hamilton with Ferrari's Sebastian Vettel, the winner in Singapore, finishing third in an exact repeat of last year's top three at Suzuka.
Hamilton now has 277 points to Rosberg's 229 with Vettel dropping back on 218 but refusing to give up his championship hopes until mathematically ruled out.
Lewis Hamilton celebrates Japan Grand Prix win
Image credit: Reuters
Mercedes, who have now won 11 of 14 races, moved a step closer to retaining their constructors' title with 506 points to Ferrari's 337.
"For me to come here to a race where I used to love watching Ayrton drive, to match his wins... I can't really describe it. It doesn't feel real at the moment," said a delighted Hamilton after saluting the fans from the podium.
If last year's post-race ceremonies were muted in the aftermath of the late Jules Bianchi's horrific and ultimately fatal accident, only a brief microphone failure prevented Hamilton from expressing his joy on the podium this time.
"I am so happy right now," he said, before Vettel poured champagne over his rival's head. "The team did a fantastic job this weekend, it's great to be back up here as a team with a one-two.
"The car was beautiful to drive today."
Rosberg had gone into the first two corners side by side with Hamilton but was forced wide to avoid a collision and dropped to fourth as Hamilton made his getaway.
Lewis Hamilton and Nico Rosberg in action at start of Japan Grand Prix
Image credit: Reuters
"Lewis just got a better start, fair play and it was a good battle into turn two," said the German. "He had the inside and just made it stick and that was the end of it there. Then it was great to fight to second place.
"Second was the best possible after that so I'm happy with the fightback."
Ferrari's Kimi Raikkonen was fourth with fellow-Finn Valtteri Bottas fifth for Williams.
Germany's Nico Hulkenberg was sixth for Force India, with the Lotus duo of Romain Grosjean and Pastor Maldonado seventh and eighth in a boost for the financially-troubled team.
Dutch hotshot Max Verstappen who turns 18 next week completed his last race as a 17-year-old in the points, taking ninth place for Toro Rosso ahead of Spanish team mate Carlos Sainz.
There was disappointment and dismay for McLaren at engine partner Honda's home track, with Spaniard Fernando Alonso making his feelings painfully clear for the Japanese manufacturer on the way to 11th place.
"I am getting passed down the straight like a GP2 (car)," he exclaimed angrily after two cars went past, one on each side. "This is embarrassing, very embarrassing."
The double world champion returned to the theme later as Verstappen passed without problem to drop him out of the points: "GP2 engine, GP2 engine," he exclaimed.
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