Hamilton got the flawless start from pole position as Verstappen was slower away from second on the dirty side of the grid and saw his Red Bull come immediately under pressure from Vettel.
"We had two laps (in the final qualifying session) and they were both not good enough".
Haas driver Romain Grosjean and Williams' Sergey Sirotkin ignored the closing Hamilton in the heat of their battle for position and cost him his five-second advantage over Verstappen.
"From FP3 onwards I was shaking from anger but now I am shaking from happiness", said Verstappen.
Lewis Hamilton eased his way to an effortless victory at the Singapore Grand Prix to stretch his championship lead over Sebastian Vettel to 40 points. "It depends on the start and the first couple of laps", Vettel said.
"I had a few driveability issues again behind the Safety Car and pulling away from the pit stop was terrible, but in the end we managed it well and got the result we wanted".
Vettel finally passed Perez, but he had lost time to Hamilton, and Verstappen, who had yet to change his tyres.
Vettel immediately questioned the decision, saying: "There is no chance".
The 20-year-old apologized to his team on the radio as he left his vehicle stranded in an escape road with two minutes left in the session, a sight that will disappoint his future employers, who will hope he does not make similar mistakes next season. "These tyres will not make it to the end". But there will be questions as to whether their decision to pit Vettel when they did was based on their mishearing a radio call from Hamilton to the pits.
Vettel was instructed to give it "everything you have", and in response Hamilton was told to stop at the end of the following lap.
He managed to go even quicker early on his second run and looked to have a shot at pole after sector two, but then Verstappen's engine cut out and he was forced to abandon his run.
Vettel replied that he did not believe him, and he engineer agreed.
"The best case is to try and preserve the tyres, go long and make a one-stop work". Either way, Vettel was right in his assessment of the situation following his stop - his hopes were over. "Didn't have the pace in the race", Vettel fumed.
Vettel refused to criticise his team's strategy.
Vettel emerged from his vehicle dejected and facing an nearly insurmountable 40-point title comeback.
Kimi Raikkonen has laid the blame for a poor qualifying at the feet of the Ferrari strategists after the Finn could only manage fifth on the grid for the Singapore Grand Prix.
It is not a recipe for excitement and what drama there was in the race was provided by also-rans. It was also slightly unfair how he had been held up by drivers not getting out of the way.
Driver of the day Perez.
"I'm spent! That was a tough race, I have such great support here and we had a great start", Hamilton said after claiming victory at the 23-turn floodlit circuit for the fourth time in his career.