Verstappen's closest title rival, McLaren's Lando Norris, qualified third, with the Briton needing to slash the triple champion's 57 point lead and only five rounds remaining.
Ferrari's Charles Leclerc, winner in Texas last weekend in a Ferrari one-two, will start in fourth place with the Mercedes pair of George Russell and Lewis Hamilton fifth and sixth respectively.
Kevin Magnussen qualified seventh for Haas with Alpine's Pierre Gasly eighth and Alex Albon ninth for Williams. Haas's Nico Hulkenberg completed the top 10 on the grid.
Red Bull's home favourite Sergio Perez continued his dire run of form with 18th place on the grid, his time nearly eight tenths of a second slower than Verstappen's best effort in the first phase.
"Every time I tried to brake I just put too much energy through the tyres and that makes it very tricky for me to stop the car," said Perez. "It's for the last three races where I cannot stop the car.
"I'm having to modulate quite a lot my braking and that's something we can see in the data, but we are not able to fix it at the moment."
McLaren's Oscar Piastri, who had been fastest in final practice, was the other immediate shock with the young Australian only 17th, while Norris sailed over the first hurdle with the quickest lap.
"It's a tricky circuit but I don't think today was down to it being tricky, I just made a very poor mistake and that was it," said Piastri.
With Ferrari on the rise in the constructors' championship, only eight points behind Red Bull and a further 40 adrift of McLaren, Perez and Piastri's grid positions were a serious blow to their respective teams.
The second phase ended prematurely with 10 seconds remaining when Yuki Tsunoda crashed his RB, in a desperate bid to get back in the top 10 after the two Haas drivers had pushed him down to 11th, with teammate New Zealand's Liam Lawson 12th.
Two-times world champion Fernando Alonso qualified his Aston Martin 13th for what will be the 43-year-old Spaniard's record 400th race.
Franco Colapinto, the Argentine rookie who has impressed for Williams, will line up 16th.
