Three-time world champion Verstappen will begin his title defence from first place on the grid in Sakhir after his 1min29.179sec final flying lap eclipsed main threat Leclerc by 0.228s.
Leclerc's session-topping Q2 run, a 1m29.165s, would have been quick enough to deny Verstappen the top spot. However, the Ferrari driver dropped time during the final sector.
The Monegasque put this down to Ferrari 'losing the rhythm' with its tyre strategy that left Leclerc to wade into the last part of the battle with a scrubbed set of soft Pirellis.
Leclerc explained: "In Q2, I did a [1m29.1s lap] which was more or less the lap time that Max did in Q3. So, it was in the car.
"Just, I think we lost a little bit the rhythm with a used set of C3 [tyres] in Q3. Then you have to re-adapt to the new tyres, and I lost a little bit there. But all in all, it's been a positive qualifying."
Leclerc, who claimed pole in Bahrain in 2019 and 2022, reckoned that the new SF-24 had not properly found its grove until qualifying, when it finally settled in a "sweet spot".
He added that, despite missing out on the top spot, Ferrari could head into the race knowing it was better off than the first blows of the 2023 campaign when he qualified third for the season-opener.
"I'm a bit disappointed," said Leclerc. "We did a good qualifying.
"It's been a tricky weekend until now. We were trying quite a few things in FP1, FP2, FP3. Then I found the sweet spot in qualifying.
"Q1 was a bit tricky. Unfortunately, we put two new sets of softs, which compromised a little bit the Q3. But all in all, it's quite a good qualifying to start the year.
"We are in a better place compared to a year ago, so that is good. Now, we have to see the race pace.
"I'm confident we did a step forward. But we have to wait and see how much of a step forward we did [in race trim]. We really think that Red Bull is still ahead by quite a bit in the race."
