George Russell put in a late flyer to join Sainz on the front row, with the Mercedes driver splitting the Ferraris as Charles Leclerc qualified third with McLaren’s Lando Norris fourth. The pole was a second in a row for Ferrari and Sainz.
Red Bull's runaway Formula One championship leader failed to make the top 10 in qualifying, with team-mate Sergio Perez also falling short.
The Dutch 25-year-old, record winner of the last 10 races in a row, was dumped out of the second phase along with Mexican Perez. For Ferrari’s Sainz, it is back-to-back poles after the Italian GP two weeks ago.
"That was ... shocking, absolutely shocking experience," Verstappen said over the team radio after qualifying 11th and being pushed out of the top 10 at the end of the phase by AlphaTauri stand-in Liam Lawson.
Perez, 145 points behind Verstappen in the standings but still his closest title rival, qualified only 13th after a late spin.
Red Bull have won every race this season and a record 15 in a row dating back to last year.
Additional reporting by Reuters.