The Red Bulls of Verstappen and Daniel Ricciardo, who was third quickest, look the most likely to upset Vettel's plans, but it could be a long night for Hamilton on the tight, corner-heavy circuit where overtaking is notoriously tough.
"I think there was damage on the vehicle already and then it didn't matter, to be honest", the German told Britain's Channel 4 television.
Mercedes expected to struggle in Singapore relative to Ferrari, but the appearance of Red Bull Racing between the two title-contending teams could make the weekend particularly costly points-wise for the Silver Arrows.
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 auto.
But it was Vettel's withdrawal that handed Mercedes driver Hamilton the initiative as the Briton, who started fifth on the grid, led after the safety auto went back in.
And then it all went wrong.
Further round the lap, Vettel, whose auto was not fatally damaged in the incident lost control and spun out.
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"For sure, it's bitter but it's done", said the four times Singapore GP victor, whose retirement ended a run of 18 successive points finishes.
Hamilton surged past Vettel and took the lead of the race.
When asked by TV crews who was to blame for the crash, Verstappen said: "Mainly Sebastian".
"That was the most frustrating thing, frustrating not to get that first win here. I'm trying", he said afterwards. "Today, I'll accept a little bit of defeat but there's still a lot to play tomorrow. I knew we had it in us".
Spaniard Carlos Sainz, who will move to Renault next season, finished fourth for Toro Rosso to score the best result of his career.
With seven points the difference between first and second, even finishing runner-up to Vettel on Sunday would see Hamilton drop four points behind the German.
Stoffel Vandoorne secured seventh, followed by Lance Stroll in eighth and Romain Grosjean in ninth place.
Esteban Ocon qualified the second Force India auto fourteenth, ahead of Romain Grosjean's Haas.