Verstappen's best final time of one minute 29.179 seconds under the Sakhir floodlights was slower than Leclerc's 1:29.165 in the second qualifying phase, but the Ferrari driver was unable to repeat it when it mattered in the third and decisive top-10 shootout round.
Leclerc ended up 0.228 slower than the Dutch driver.
Mercedes' George Russell qualified third, 0.306 off Verstappen's benchmark, and Ferrari's Carlos Sainz, who will make way for seven-time world champion Lewis Hamilton next season, was fourth-fastest.
Bahrain and Saudi Arabia, both held under lights and the first two rounds of a record 24-race championship, are being run on Saturdays to accommodate Ramadan, which starts on the evening of March 10th.
Friday’s pole was the 33rd of Verstappen’s career and puts him on course to open his pursuit of a fourth consecutive title just as he left off when winning his dominant third.
It also came as a welcome reprieve for his Red Bull team, who have been in the headlines due to an independent investigation into team principal Christian Horner that on Wednesday cleared the Briton of allegations of misconduct, which he had denied.
"The track had a lot of grip but with the wind, it's been tricky to get the whole lap together," said Verstappen, winner of 19 of 22 races last season.
"Q3 was difficult, but happy to be on pole. To be honest it was a little unexpected but in qualifying the car came to us."
At the end of the session, Verstappen appeared under the impression that he had not done enough and apologised over the radio to race engineer Gianpiero Lambiase.
"Nothing to be sorry about Max. A very good start. Two-tenths clear of Charles and three-tenths clear of George," said Horner.
Red Bull's Sergio Perez will start fifth with Aston Martin's Fernando Alonso sixth and McLaren's Lando Norris and Oscar Piastri seventh and eighth.
Hamilton will start his final season with Mercedes in ninth place with Haas's Nico Hulkenberg a surprise 10th for the U.S.-owned team.
"It's not the greatest of feelings," Hamilton told Sky Sports television.
"But I am excited to be here... it's amazing for us to have a car that we can fight with. It just really lights the fire within us drivers."
Renault-owned Alpine endured a bruising session with French drivers Esteban Ocon and Pierre Gasly lining up on the last row of the grid.
