Seven-time champion Lewis Hamilton made up ground for Mercedes on his final run but never looked like securing a record-extending 104th pole and starts from a disappointing fifth place. He is behind Red Bull's Sergio Perez and Ferrari's Carlos Sainz Jr. in third.
Hamilton's ex-teammate Valtteri Bottas made it a sore day for Mercedes by placing sixth for his new team Alfa Romeo, while his replacement George Russell was only ninth after a poor last run.
Mercedes looks to be struggling as others unexpectedly improve.
Haas uses Ferrari engines and is looking good, with the re-hired Kevin Magnussen showing it was maybe a mistake to fire him in 2020. He starts in seventh place in his comeback race after replacing the axed Russian driver Nikita Mazepin.
Ferrari set the leading times in the final part of qualifying, known as Q3, with Mercedes lagging around 1.5 seconds behind the Ferraris. But already it wasn't looking good for Mercedes in Q1 with Russell ninth and Hamilton 10th.
It was even worse for McLaren's Daniel Ricciardo, who has won eight races in his career.
The experienced Australian won the team's only race last season but couldn't even get into the second part of qualifying known as Q2. He starts in a dismal 18th place while teammate Lando Norris, who got four podiums last year, is not much further up in 13th.
Verstappen led Q2 from Sainz Jr. and Leclerc as Mercedes again trailed the top drivers.
"It was a good start to the new era," Verstappen said. "It was a really close battle with Carlos and Charles."
Earlier, Verstappen narrowly led the third and final practice ahead of Leclerc and Perez.
Verstappen posted the fastest time in all preseason testing and led second practice ahead of the Ferraris, which were also second and third in the first practice.
Mercedes expressed severe doubts about the pace of its car in testing. After Friday's two practice runs Hamilton had already ruled out victory despite being F1′s record holder with 103 GP wins.
Hamilton has won races where he's started from far lower than fifth, but there are doubts his car can match his driving this time.
Qualfying results
1. Charles Leclerc, Ferrari, 1 minute, 30.558 seconds.
2. Max Verstappen, Red Bull, 1:30.681.
3. Carlos Sainz Jr, Ferrari, 1:30.687.
4. Sergio Perez, Red Bull, 1:30.921.
5. Lewis Hamilton, Mercedes, 1:31.238.
6. Valtteri Bottas, Alfa Romeo Ferrari, 1:31.560.
7. Kevin Magnussen, Haas Ferrari, 1:31.808.
8. Fernando Alonso, Alpine Renault, 1:32.195.
9. George Russell, Mercedes, 1:32.216.
10. Pierre Gasly, AlphaTauri RBRT, 1:32.338.
Eliminated after second session
11. Esteban Ocon, Alpine Renault, 1:31.782.
12. Mick Schumacher, Haas Ferrari, 1:31.998.
13. Lando Norris, McLaren Mercedes, 1:32.008.
14. Alexander Albon, Williams Mercedes, 1:32.664.
15. Guanyu Zhou, Alfa Romeo Ferrari, 1:33.543.
Eliminated after first session
16. Yuki Tsunoda, AlphaTauri RBRT, 1:32.750.
17. Nico Hulkenberg, Aston Martin Aramco Mercedes, 1:32.777.
18. Daniel Ricciardo, McLaren Mercedes, 1:32.945.
19. Lance Stroll, Aston Martin Aramco Mercedes, 1:33.032.
20. Nicholas Latifi, Williams Mercedes, 1:33.634.