After leading FP3, Q1 and Q2, Verstappen looked in good shape for pole, but ultimately could not match Vettel's stunning final effort in Q3.
Mercedes has been dominant all season long, but their difficulties under the lights of the Singapore GP prevailed on Saturday qualifying as Ferrari and Red Bull made sure the erstwhile leaders are stuck in the third row once the race starts on Sunday.
"I definitely didn't anticipate Ferrari would be as strong as they were". I struggled in final practice and I cried probably as loudly as them [the crowd - when I got pole] - it was unbelievable.
"It was unbelievable, I'm still full of adrenaline".
"All weekend has been a good build up, getting faster and faster and finding a smooth rhythm so to come away with second is a really good result", Verstappen said.
"I'll take the fourth place, because if you purely look at where we were before qualifying, it could have been a lot worse", Raikkonen said. Tomorrow is a long race and the Red Bulls are very quick.
"We knew that today would be tough", he said.
"In theory it should be a bit better here than Monza but I think it will be close", Vettel told reporters.
"It is a shame we couldn't put it on pole", Verstappen added.
Hamilton is distinctly second favourite against his title rival at the twisting, turning and stiflingly hot Marina Bay street circuit, which plays to Ferrari's strengths and where Vettel has won four of the nine races.
It's still better than the original contract that I had", Bottas said."As always with my career in F1, it's going to be completely up to me. I will accept a little bit of defeat, but tomorrow I am still confident we will get victory.
"I think overall we wanted more grip but that's the normal story".
"So far this year, we have seen the pendulum swing according to circuit type".
While Sebastian Vettel turned in one of the qualifying performances of the season to beat the quick Red Bulls, Raikkonen was almost 0.6s behind his teammate. I gave it everything and more.
On one of Formula One's hardest tracks for overtaking, even as talented a driver as Hamilton will be pushed to secure a podium.
"I think the start is an opportunity, strategy is an opportunity, safety cars, who knows?"
Sebastian Vettel had set a purple first sector on his initial flying lap before catching traffic and being forced to abandon the lap. His teammate Stoffel Vandoorne is ninth and Carlos Sainz rounds out the top 10.