The championship leader had stretched his lead to around three seconds when, on lap 14, Vettel was first to pit for ultrasoft tyres, but it soon looked an ill-judged move as he rejoined behind the slower Force India of Perez.
His teammate Valtteri Bottas was fourth ahead of Ferrari's Kimi Raikkonen and Red Bull's Daniel Ricciardo.
"Great job everyone, what a weekend. keep pushing, keep pushing, we've got this", Hamilton told his team over the radio soon after crossing the line at the end of the 61st lap. "I think from Lewis' side, for me that was stardust; the most epic lap I have ever seen from him".
"I think obviously the gap is quite big. We needed a mega outlap, I did what I could, but it wasn't enough". For us today, the way we composed qualifying, I think it was hard to get a rhythm.
"The vehicle is then not able to find a gear, so I nearly stalled".
"Yesterday was looking really good for us and then we came into today, we made some changes and we didn't have a good (practice) session".
He said: "We tried to be aggressive in the beginning, and it didn't work out".
Hamilton got the ideal 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.
While Vettel was left to question his team once again this season - and for the second time this weekend after a less-than-perfect qualifying session - Hamilton's only worrying moment was caused by back markers at about two-thirds distance.
Mercedes driver Lewis Hamilton cruised to victory in the Singapore Grand Prix to strengthen his hold on this year's World Championship.
But Vettel remains confident that the race could still come to him and Ferrari, with long-run simulations from Friday's free practice running putting Ferrari's race pace at 0.2s per lap quicker than Mercedes - although Red Bull were a further 0.2s quicker than them.
Pole in 2017 was set by Sebastian Vettel - he took third place this time around - with a 1:39.491 but such is the improvement between years that this time would have seen him qualify P15 in 2018. I got the call to box and that's what we went for. I think it was definitely there for our grasp and the way qualifying happened, it wasn't any more.
The report, and the tweet which went with it, did not go down well, with fans accusing the Italian team of being "sore losers", while others questioned why they hadn't spiced it up with a better strategy.
All the top teams will want to just do one stop and so anything that could make Mercedes have to operate outside their comfort window could be a benefit to Vettel.
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