The Dutch youngster, fresh off his seventh grand prix win last weekend in Germany, narrowly edged out Mercedes pair Valtteri Bottas and Lewis Hamilton, in second and third.
It was a landmark achievement in the sport as Verstappen becomes the 100th different driver to secure a pole position in Formula One.
"It's incredible," the 21-year-old told Sky Sports. "This one was still missing, and the car felt good all weekend. Of course, you know, it's always going to be hard in qualifying. ... A big thank you to the team -- the car was flying out there in qualifying, it was incredible.
"We're very happy about today, but there is still a race, and that's, at the end of the day, the most important. But for me, today was an important one, a very nice one and also a great one for the team."
There had been concerns about whether the condition of the track would affect final practice and qualifying after officials were forced to lay down cement dust to improve grip following an oil spill.
The final practice session was delayed as marshals tried to make the track safe, though aside from providing some dramatic photos, it barely affected them.
Championship leader Hamilton couldn't find enough pace to get on the front now, finishing 0.197 seconds further back, but comfortably saw off the struggling Ferrari cars of Sebastian Vettel and Charles Leclerc.
It was another erratic afternoon from the young Monegasque driver, who put his car in the wall on the final corner during the first qualifying session, leaving it in need of a new rear wing.
Leclerc took full responsibility for his mistake, though that is now two errors in consecutive weekends, following his spin and crash Sunday in Germany.
It briefly looked as though Bottas -- who finished just 0.018 seconds back -- would steal pole position, but Verstappen nailed his final few corners, much to the delight of the thousands of traveling fans in orange.
The Dutch have followed their national hero in huge swathes throughout the European leg of the season, and Verstappen said their support spurred him on to secure a maiden pole at his 93rd attempt.
"The margins are so tight around here, but Max was on fire," Christian Horner, Red Bull team principle, told Sky Sports. "He was the quickest in almost every section of qualifying.
"The last lap was stunning. He needed to nail that last corner because Valtteri was slightly ahead. It's fantastic for him to get his first pole -- it's a great team effort to get us on the front row."
As Verstappen's engineer told his driver after qualifying: "Better late than never."