The Dutchman, who claimed his first win of the F1 season at the Bahrain Grand Prix held in Malaysia last weekend, was in imperious form again as his Red Bull showed further signs of progress.
"It is always close in Singapore, your lap - you are pushing as close as you can to the walls. I did not expect this, very happy to be first," Verstappen said.
Russell saved his best until last but was unable to topple the four-time world champion, finishing 0.120 seconds adrift as he bumped Ferrari's Charles Leclerc down to third.
Piastri claimed fourth for Saturday's 21-lap dash, ahead of McLaren teammate Lando Norris and Ferrari's Lewis Hamilton.
Runaway championship leader Kimi Antonelli was off the pace throughout the session and could manage only seventh – 0.693sec off the pace to raise further doubts over the upgrade Mercedes brought last weekend.
Antonelli has one hand on the title after team-mate Russell's power-unit failure in the closing stages last week gave the Italian an 84-point lead with just seven rounds to run.
Russell, running the Mercedes car without the upgrade, will start the main race on Sunday from the back of the grid after taking a new power unit, in a further blow to his slender title hopes.
Verstappen, however, does face a stewards' investigation for overtaking under yellow flags.
Hamilton was on the radio to accuse his old rival of overtaking him as the flags waved following Sergio Perez's contact with the barriers and resulting debris in the opening qualifying run.
There was a delay to the start of the second part of sprint qualifying after the FIA discovered an issue with the timing system, with some times in the opening session not initially registered.
Leclerc led Hamilton in a Ferrari one-two in a second session delayed by 16 minutes after Verstappen had topped the first, to hint at an open fight for pole.
So it proved but it was Verstappen who pulled the stellar lap out the bag in the closing stages and the four-time world champion will hope to continue his step forward with sprint victory on Saturday.
Mercedes team principal Toto Wolff said earlier that any claims the team would favour Antonelli over Russell in the title race were "brainless".
Wolff was responding after engine failure for Russell at the Bahrain Grand Prix in Malaysia last week took his teammate Antonelli a big step closer to becoming F1's youngest-ever champion.
"They're brainless, whoever thinks that. I mean, it's completely nonsensical. We've had it in the past with Lewis (Hamilton) fans. I mean, literally, I don't know what's going on," Wolff said.
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