Ferrari's Charles Leclerc (26) joined the Dutch driver on the front row with the Aston Martins of Lance Stroll (24) and Fernando Alonso (42) on the second row.
The session was halted as the sky turned dark as night, with lightning flashes as the wind picked up and rain lashed down. The governing FIA said the session would not be re-started.
Verstappen was quick out of the pits as storm clouds loomed, getting a flying lap in to secure provisional pole before gusting winds, rain and flashes of lightning halted the track action.
"We didn’t know when it would hit in qualifying, we thought it would hit. This is of course insane weather," said the Dutchman, who secured his third title in Qatar last month.
McLaren's Australian rookie Oscar Piastri (22) had already skidded off onto the grass, triggering yellow flags.
With the rain expected imminently, Verstappen overtook the Mercedes of last year's winner George Russell as they exited the pit lane.
Leclerc, who had been on pole for the two previous races, was 0.294 slower.
"In my whole career I have never experienced something like that. From Turn Four onwards there was no rain. But the car was extremely difficult to drive, no grip," said the Monegasque.
"I was thinking about coming in at the end of the lap but I finished it and it was P2. So a really good surprise. A very weird one for everyone at the track."
The governing FIA stopped the clock with four minutes remaining and said the session would not be re-started.
Mercedes' seven time world champion Lewis Hamilton (38) and Russell filled (25) the third row, with McLaren's Lando Norris (23) seventh and Ferrari's Carlos Sainz (29) eighth and Red Bull's Sergio Perez (33) ninth.
"I did the best I could, hopefully we'll have a better race," said Hamilton.
Russell said the conditions were "absolutely crazy".
"I've never, ever seen a change of weather so drastic as that," said the Briton. "I was just sliding around, I had no grip... I actually wanted to pit because I was confident I was going to be last."
Mexican Perez was forced to slow on his lap after Piastri went off.
Interlagos is hosting Formula One's final sprint weekend of the season, with Sunday's grand prix grid set on Friday while Saturday's schedule features a sprint qualifying 'shootout' followed by a standalone 100km race.
