Verstappen's hopes of a record-extending 11th successive victory looked a long shot on a city circuit where overtaking is never easy
Carlos Sainz put Ferrari on pole position for the Singapore Grand Prix on a shocking Saturday for dominant Red Bull whose record run of 15 wins in a row appeared to be reaching the end of the road.
The pole was the Spaniard's and Ferrari's second in succession as well as the Italian team's third in four races.
Red Bull's runaway championship leader Max Verstappen and team mate Sergio Perez both failed to make the top 10 shootout, an astonishing turnaround for a team that had been in a league of their own but suddenly looked lost.
Verstappen's hopes of a record-extending 11th successive victory looked a long shot on a city circuit where overtaking is never easy.
The Dutch 25-year-old qualified 11th but was facing a potential further drop after stewards' enquiries for allegedly impeding.
"That was ... shocking, absolutely shocking experience," Verstappen said at the end of phase two after realising he would play no further part in qualifying.
Perez qualified only 13th for what will be his 250th Formula One start.
Without the Red Bulls on track, rivals had everything to play for and Sainz made his lap count with a best time of one minute 30.984 seconds.
Leclerc looked like securing a front row sweep for the Italian team but Russell came through in 1:31.056 to beat the Monegasque by a mere 0.007.
McLaren's Lando Norris will start fourth with Mercedes' Lewis Hamilton fifth on the grid and Haas's Kevin Magnussen sixth.
Aston Martin's Fernando Alonso starts seventh with Alpine's Esteban Ocon eighth, Haas's Nico Hulkenberg ninth and AlphaTauri's Liam Lawson 10th.
The pole was a second in a row for Ferrari and Sainz.
Aston Martin's Lance Stroll crashed heavily at the final corner in the dying seconds of the opening session, bringing out the red flags and delaying the start of the second phase.
Stroll clambered out of the wrecked car, which smashed into the barriers almost head-on and so hard that the front left wheel was ripped off, and was taken to the medical centre for checks.
The red flags caught out McLaren's Australian rookie Oscar Piastri, whose final flying lap had to be aborted and left him 17th on the grid at a tight track where overtaking is a challenge.
"It should have been enough to get through," he said of his lap up to that point. "It makes our evening tomorrow very difficult."