Norris said: “I was finding it tough to progress much and the guys around me were getting quicker and quicker putting me under pressure. But it was good enough for pole. I felt confident all weekend. Maybe not so much in qualifying, but we got the job done.”
Verstappen, who had been unhappy with his car in Friday practice, said: “The whole of qualifying went quite well. We managed to improve the car.
“I am happy to be on the front row if you look at where we came from yesterday. Everyone only has one lap so you don’t want to overdo it. I take second, I’m happy with that.”
Hamilton’s third place is his best qualifying since he was second on the grid at the British Grand Prix.
He said: “Qualifying has been a disaster for me all year long and I have just been working and working and working trying to get myself back up there and all of a sudden the car came to me for the first time in a long time in qualifying.
“We have been moving up and down on balance. We have changed everything and the mechanics have been faultless and I hope we are in a good position to fight for the front tomorrow.”
Hamilton edged out Russell by just 0.026secs, while Piastri ended up 0.428secs slower than Norris.
The Australian has promised to help Norris in his title fight with Verstappen if he can, but starting three places behind the Red Bull will make that difficult.
Leclerc had vied with Norris for fastest time throughout Friday but said that Ferrari had a problem with the blankets which are used to heat the tyres to the correct temperature.
“A very bad job is our result today,” Leclerc said. “For whatever reason, I don’t know if it is our mistake or a component mistake but the blanket was not working properly.
“We had completely cold tyres on the fronts and never really recovered the temperature. Got into Turn One, braked, locked the front wheels, did track limits and that was it.
“Considering how important it is in Singapore, all the work we have done to be ready in Q3, I consider it quite crazy we do something like this.”
But team principal Frederic Vasseur said that, while the tyres had lost some temperature in the pit lane, they were in the right window by the time Leclerc started his flying lap.
Vasseur added of Leclerc running wide at the first corner: “You know that you only have one lap, you have to push, you are on the limit, and he crossed the line by a couple of centimetres. It is part of the game.”
Sainz, meanwhile, was fined 25,000 euros (£21,000) for crossing the track and pit lane without permission after his crash.
