Hamilton controlled the race from then on, leading every lap as he finished ahead of Daniel Ricciardo's Red Bull and the second Mercedes of Valtteri Bottas was third.
"I've got no idea -- and that is the concern I've always had with this race", Romain Grosjean told Autosport.com earlier, when asked if it would be safe to race in the rain.More news: Engine options 'limited' for Red Bull
The four-time Singapore GP victor then added to Sky Sports F1: "I didn't see that much". But no driver was deemed responsible and no further action was taken.
Following a massive downpour several hours beforehand, more heavy showers soaked the Marina Bay circuit just before the race which started 8 p.m. local time (1200 GMT).
"I capitalized on the incident", Hamilton said.
"You might have to carry us out of the cars tomorrow but I'm sure I'll have a very strong race and get some big points". "I'm trying", he said afterwards. The race is a 192-mile contest that will run 61 laps around the track.
"I had an average start and then went to the left trying to fend off Max and the next thing I get a bump on the side and see Kimi's vehicle".More news: Georgia teen's death at LSU frat house possible hazing incident
The race was far from over for Hamilton however, with rain falling intermittently and Marcus Ericsson's crash forcing the safety auto to return on lap 38.
Vettel was away slowly from pole, and looked to squeeze Verstappen, who had started alongside him in second.
"Today I'll accept a little bit of defeat but there's still a lot to play for tomorrow", Ricciardo said.
Hamilton had a healthy advantage of 9.6 seconds when Sauber's Marcus Ericsson spun and stopped on Anderson Bridge, bringing out a third safety auto and wiping out the Briton's lead.
Mercedes declined to pit Hamilton under the safety vehicle but after the restart, he reeled off a string of fastest laps on the slowly drying track, extending his lead over Ricciardo.More news: When I Was Nominated: Emmy Awards Edition- Stephen Colbert
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