Verstappen, who had never qualified within the top three before today at Interlagos, was quickest in all three sessions of qualifying as well as FP3 earlier on Saturday.
Charles Leclerc did clock the fourth-best time in Q3 but will drop 10 places due to a grid penalty for swapping out his engine, meaning third-placed Lewis Hamilton will be joined by his teammate Valtteri Bottas on the second row of the grid.
Drama at McLaren early-on on Saturday afternoon, with Sainz failing to set a time in Q1. During his out lap for his first run, he lost power and dived straight back into the pitlane, where the mechanics got to work. However, they didn't get it back on track in time to set a time, meaning Sainz will start from the back of the grid for the race on Sunday.
At the top, it was Verstappen who set the pace as he topped the timesheets, beating the Ferrari of Leclerc to it as Alex Albon surprisingly was third. Another surprise was Kevin Magnussen in P7, leading all midfield cars.
Verstappen again set the pace in Q2, a session in which the second runs were pretty much useless because of the dropping temperatures in the middle of it. The first run was again Verstappen's, with Leclerc again following. The Monegasque was the only one who set his time on the medium tyre, meaning he'll start on them for the Grand Prix.
For the first time in half a season, both Haas cars made it into Q3 as Romain Grosjean this time led the midfield cars, with Magnussen in ninth. The other midfield cars to make it out were Pierre Gasly and Kimi Raikkonen, meaning Norris failed to get in. He was P11, beating the Renaults in P12 and P14. Antonio Giovinazzi was wedged in between, with Sergio Perez being the slowest car in the session.
Again, it was Verstappen who struck first, setting the quickest time after the first run, despite the 22-year-old coming on team radio to say it wasn't an optimal lap. He improved on his lap by over a tenth of a second on his second and final run, further sealing his pole position.
Vettel was second to his Aston Martin Red Bull Racing counterpart, beating Hamilton and Leclerc to the front row.
Bottas was fifth and Albon sixth, with Pierre Gasly leading the midfield for Toro Rosso as he amazingly qualified seventh. Grosjean, Raikkonen and Magnussen completed the top 10 in that order as Haas look to score points again for the first time since Russia.