Hamilton took the lead early from teammate and pole sitter Nico Rosberg and cruised to his eighth win of the 2015 Formula One season.
The result leaves Hamilton 48 points clear of Rosberg in the title race, with Vettel a further 11 points adrift with five rounds remaining.
Hamilton had been denied his chance of taking pole position in Saturday's qualifying after Daniil Kyvat's spectacular crash brought the session to a premature finish.
But he made the faster start off the grid and swept past Rosberg to assume control, with his German rival slipping back to fourth place before moving back through the field into second spot.
It was Hamilton's 41st career F1 victory, drawing him level with the great Ayrton Senna in the all-time list, and his second straight at Suzuka, one of his favorite tracks.
"To come here, where I used to love watching Ayrton drive, and match his career wins, is amazing for me," he said at the victory presentation.
"It was important for us to strike back. We didn't bring our 'A' game in Singapore and we had to bring it today."
Behind the front runners, Kimi Raikkonen took fourth in the second Ferrari, with Valtteri Bottas in fifth for Williams and Nico Hulkenberg sixth in the Force India.
But it was another dismal afternoon for McLaren, with Fernando Alonso complaining about the lack of power from his Honda engine as he took 11th.
Teammate Jenson Button was further back in 16th as he ponders his future in Formula One.