Track conditions have been difficult to read from lap to lap on the temporary course in sizzling tropical conditions, with the qualifying soft tyres prone to sudden and extreme overheating.
The battle for pole appeared delicately poised after the first exchanges of the top-10 shootout, with Verstappen seizing back the initiative after Leclerc had topped Q2.
But rather than a climax, the session flopped, with most drivers finding their tyres had fallen out of the window in the sweltering heat, leaving them unable to improve.
Verstappen’s first lap proved to be his best, with his time of 1 minute 27.241 seconds surviving to the end of the session to secure him pole.
“I don’t know what it is, every single year we come here I find it extremely difficult to be consistent with the car feeling, with the tyre feeling over one lap,” he said.
“It’s not the most enjoyable lap of my career just because of how slippery it is. You’re not very confident on the lap.
“But we’re on pole, and that’s the most important.”
Leclerc ended up 0.141 seconds adrift, but the Ferrari driver was confident he had the race pace to be a contender on Sunday.
“It felt so much on the limit,” he said. “When we started to push for the last one or two tenths, we started to lose the tyres in sectors two and three. Today that’s where we lost a little bit of time.
“However, the race is long tomorrow. This morning we showed good pace, so I hope tomorrow we can put Max under a bit more pressure.”
Leclerc will count on teammate Carlos Sainz starting from third to help him try to navigate past the title-leading Dutchman in the grand prix, the Spaniard hoping his starting position could pay dividends.
“You always finish the lap and feel like you could’ve gone so much faster having a cleaner lap, but it’s almost impossible to put in a perfect clean lap around here,” he said.
“That’s why being P3, clean side of the road tomorrow, could be a good place to start.”
Sergio Pérez, pole-getter in Miami last year, will start fourth after falling 0.219 seconds short of his teammate in P1.
McLaren teammates Lando Norris and Oscar Piastri qualified fifth and sixth, the Briton beating the Australian by just 0.081 seconds.
Mercedes struggled to seventh and eighth, with George Russell 0.04 seconds quicker than Lewis Hamilton after both ran out of soft tyres for their final laps.
Nico Hülkenberg took Haas into the top 10 for the third time this season in ninth, while Yuki Tsunoda completed the top 10 for RB.
Lance Stroll will line up 11th as the lead Aston Martin car despite failing to improve on his Q1 time.
Alpine teammates Pierre Gasly and Esteban Ocon qualified an improved 12th and 13th for the team’s best combined result all season.
Thai driver Alex Albon qualified 14th for Williams ahead of a surprisingly lacklustre Fernando Alonso in 15h.
Valtteri Bottas will start the race 16th ahead of Logan Sargeant.
Daniel Ricciardo qualified 18th ‒ a shock result after the Australian qualified and finished fourth for the sprint race ‒ but will start last with a three-place grid penalty carried over from the Chinese Grand Prix.
The penalty will promote Kevin Magnussen and Zhou Guanyu to 18th and 19th, though both are facing post-session investigations, Magnussen for unsportsmanlike behaviour in the sprint and Zhou for crossing the pit exit line.