Hamilton avoided the trouble and progressed from fifth on the grid to first, ahead of Red Bull's Daniel Ricciardo, as the cars race finally restarted after a safety auto.
The race, the first to be hit by rain in the decade that Singapore has hosted Formula One, had started in treacherous conditions after a formation lap behind the safety vehicle.
"Even before the first [safety car], we could see were losing an bad lot of oil pressure in the gearbox, so we were thinking, "crikey, this is only going to go to half-distance", Horner told Sky Sports.
However, the Ferrari driver Vettel is known as one of the most consistent drivers in the South-East Asian track.
"I still believe that our concept is the right concept", he said.
The race was far from over for Hamilton however, with rain falling intermittently and Marcus Ericsson's crash forcing the safety vehicle to return on lap 38.
"I capitalised on the incident".
After a hesitant start, the four-time F1 champion veered hastily left as he tried to counter Verstappen's strong start.
Singapore Grand Prix 2017
The three-time world champion has a slender three point lead over rival Sebastian Vettel following his victory in Monza. He is now sixth in the point standings and been retired in six different races this year.
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When asked by TV crews who was to blame for the crash, Verstappen said: "Mainly Sebastian".
The FIA has said the incident will be investigated after the race. "It gave me time to see what would happen".
Daniil Kvyat, Marcus Ericsson (both accidents), Hulkenberg and Kevin Magnussen (both mechanical) joined the big names on the DNF list before the end of the race - which was shortened from the scheduled 61 laps to just 58 inside the two-hour time limit by the various safety vehicle interventions - but there was little drama out front, with the biggest question marks surrounding the point at which it was judicious to move from grooved rubber to slicks.
"Then the next thing there was a bump on the side and I saw Kimi's vehicle, so I don't know what happened".
The safety vehicle came out again shortly after, as Daniil Kvyat crashed his Toro Rosso.
Vettel was away slowly from pole, and looked to squeeze Verstappen, who had started alongside him in second.
It made no difference here, as Hamilton won by 4.5 seconds.
Team-mate Daniel Ricciardo claimed third and Kimi Raikkonen may be called upon to hold up Hamilton, having qualified in fourth, with Valtteri Bottas alongside his fellow Silver Arrow in the third row.