The accident brought an early end to the race, which was red flagged and finished under the safety car, and the result backdated to lap 44.
Hamilton thus led home team mate Nico Rosberg, Red Bull duo Sebastian Vettel and Daniel Ricciardo, McLaren's Jenson Button and the Williams cars of Valtteri Bottas and Felipe Massa. Force India pair Nico Hulkenberg and Sergio Perez finished eighth and tenth, sandwiching Toro Rosso's Jean-Eric Vergne.
It had been Rosberg who led in the early stages, although the first attempt to start the race behind the safety car had to be aborted because of the conditions after only two laps. It was restarted after a 25-minute delay, and the safety car stayed out until lap nine. Once under normal conditions, the race quickly developed into the anticipated duel between Rosberg and Hamilton.
For the next 19 laps the Briton pursued his team mate, increasing the pressure despite a scare at Turn 1 when he ran wide and over the artificial grass when, he admitted, he had left his DRS open. Going into the same corner two laps later Hamilton's persistence finally told: he got a run on Rosberg down the straight, forcing the German to defend the inside line, which allowed Hamilton to sweep around the outside in spectacular fashion. Once into the lead, he began pulling away immediately.
As Rosberg consolidated second place, attention turned to the battle between Button and the Red Bulls. The McLaren driver was the first driver to pit for intermediate tyres, coming in on lap nine, and the decision paid off as he jumped up to third by the time everyone but the Mercedes had followed suit and switched to the green-marked inters.
Vettel and Ricciardo gradually closed in, however, with the Red Bulls the fastest cars on track at the halfway stage. Button eventually claimed an honourable fifth, his advantage having been lost when his car's steering wheel had to be changed during his final pit stop - with a problem which also affected his team mate Kevin Magnussen, who finished well down in 14th.
Vettel, meanwhile, dropped to fourth as a result of a late stop for fresh tyres, but with the race result being backdated was elevated back into third, ahead of team mate Ricciardo.
Williams' challenge was blunted early as the FW36s proved a handful in the wet - a trait underlined by the fact Ricciardo was able to pass both Valtteri Bottas and Felipe Massa around the outside in the Esses. The duo hung on for fifth and seventh respectively, moving Williams further ahead of Ferrari in the constructors' stakes.
The Scuderia failed to score a point at Suzuka - the first time they have missed the top 10 in 82 Grands Prix - as Kimi Raikkonen finished 12th and Fernando Alonso retired early on with an electronic glitch.
Nico Hulkenberg finished eighth for Force India on countback, despite having rolled to a stop at the exit of the pit lane as the race was red flagged.
A fighting Vergne again overshadowed rookie team mate Daniil Kvyat to finish ninth for Toro Rosso, with Sergio Perez rounding out the top 10 in the second Force India, who now have 122 points in the constructors' championship, one point ahead of McLaren on 121.
Kvyat was 11th ahead of Raikkonen, while Sauber's Esteban Gutierrez was 13th ahead of Magnussen. Lotus's Pastor Maldonado survived many off-track moments to lead Lotus team mate Romain Grosjean home until a post-race pit lane speeding penalty dropped him behind the Frenchman.
Caterham's Marcus Ericsson, meanwhile, recovered from a spin on the first lap - while the field was running behind the safety car - to head Marussia's Max Chilton and Caterham team mate Kamui Kobayashi in the fight for 17th.
Hamilton therefore extends his lead to 10 points over Rosberg, 266 to 256, with Ricciardo third on 193 from Vettel on 139, Alonso on 133 and Bottas on 130.
Mercedes are on the brink of clinching the 2014 constructors' championship, moving onto 522 points - Red Bull are second on 332, with Williams third on 201 and Ferrari fourth on 178.