Verstappen had endured a difficult build-up to the grid-setting hour, having been way off the pace in all three practice sessions with a car that appeared to have an unpredictable balance and a reluctance to attack the kerbs.
But the Dutchman and his Red Bull Racing team rose to the challenge in time to swat away challenges from both McLaren drivers in the fight for pole.
Verstappen pipped Lando Norris to top spot after the first laps of Q3. Piastri in the second papaya machine then improved enough to put himself in position to pinch top spot for himself, but an excellent adrenaline-fuelled final lap from the reigning champion sealed the deal by 0.074 seconds.
“I’m still pumping,” he said. “The adrenaline is very, very high.
“It’s been a really difficult weekend so far, even this morning, I’m incredibly happy to be on pole here. I didn’t expect that.
“We made some final changes before qualifying. They seemed to make it a little bit better so I could push a little bit harder.”
It was Verstappen’s seventh straight pole of the year and eighth in succession, dating back to last year’s Abu Dhabi Grand Prix, drawing him level with Ayrton Senna’s eight straight poles in 1988-89.
“Thirty years since he [Senna] passed away at this track, of course I’m very pleased to get pole here.
“In a way it’s a nice memory to him. He was an incredible Formula 1 driver.”
Oscar Piastri is poised to take the first front-row start of his grand prix career after qualifying second, but the result is pending a post-session investigation into him blocking Kevin Magnussen in Q1.
The Australian was nonetheless satisfied with his performance and believed McLaren could target a second consecutive victory following Norris’s win in Miami two weeks ago.
“I think normally in the past we’d say no, but I think with our recent performances we’ve learnt to say yes,” he said. “We’ve definitely been on the pace all weekend.
“The confidence is high we can do something good.”
Norris, who stands to inherit second place from third on the grid, said he expects a tight race.
“It’s exciting we’re close, and I can’t wait for tomorrow,” he said. “We still need to get used to it, but we’re getting closer.
“It’s going to be close. It’s going to be a good race tomorrow. Hopefully it’s an exciting one to watch.”
Ferrari had hoped to be a pole contender but struggled to carry its momentum from practice and the earlier qualifying segments into Q3.
Charles Leclerc qualified 0.225 seconds off the pace in fourth ahead of teammate Carlos Sainz, who was almost half a second adrift.
George Russell led the way for Mercedes in sixth ahead of Yuki Tsunoda, Lewis Hamilton, Daniel Ricciardo and Nico Hülkenberg.
Sergio Pérez blew a shot at contending for pole with a small mistake through Variante Alta on his final flying lap, leaving him 11th and knocked out of Q2 by just 0.015 seconds.
Alpine’s Esteban Ocon will start alongside him on the sixth row of the grid, with Aston Martin’s Lance Stroll, Thai Williams driver Alex Albon and Pierre Gasly in the sister Alpine qualifying down to 15th.
Sauber duo Valtteri Bottas and Zhou Guanyu will start 16th and 17th ahead of Haas driver Kevin Magnussen, who will see the stewards after the session over allegations he was obstructed by Piastri late in Q1.
Fernando Alonso was a surprise and underwhelming elimination in 19th for Aston Martin, his first Q1 knockout since last year’s United States Grand Prix.
Alonso had been driving a hastily reassembled car after he’d crashed in final practice earlier on Saturday, but the repaired machine looked uncompetitive in his hands, leaving him unable to escaped the back row of the grid ahead of only Logan Sargeant, who ended the session with no valid time after having laps deleted for exceeding track limits.