The Dutchman, who secured his second successive Formula One title this month with four races to spare, lapped the high-speed Autodromo Hermanos Rodriguez with a fastest time of one minute 17.775 seconds.
George Russell joined him on the front row, qualifying 0.005 ahead of seven-times world champion Mercedes team mate Lewis Hamilton, with Red Bull's Mexican Sergio Perez the fourth fastest with the crowd cheering.
"It was a close one," said Verstappen, who was 0.304 faster than Russell.
"To be on pole here is of course amazing. It's a very long run to turn one so we do need a good start but anyway I think we have a quick car and that's what's most important.
"Checo (Perez) will be there tomorrow. I'm sure we have a quick race car. I hope it will be quite a fun race with a lot of action."
The pole was the 19th of Verstappen's career and he will be hoping to convert it into a fourth Mexican victory to take the outright record of most wins in a season from German greats Michael Schumacher and Sebastian Vettel, who both managed 13.
Red Bull, fined $7 million on Friday for spending more than allowed last season, have won the last eight races and 15 of 19 so far.
MERCEDES HOPEFUL
Once-dominant Mercedes, who have yet to win this year, can take hope from history with the winner of the last two races at the high-altitude circuit coming from third on the grid.
The driver on pole has not won since 2016 and Hamilton won from third in 2019.
"The team deserved more today ... I feel like it was our pole to have and it was just a terrible lap from my side, so I'm sort of kicking myself," said Russell, who felt he might have sneaked it but for a mistake.
"But no points for qualifying and excited to be back on the front row. I'll be going for it for sure so let's see what's possible."
Team boss Toto Wolff stated that he believes that this is set to be their best chance of claiming a victory.
The qualifying was Mercedes' best team performance so far in a tough 2022 spent wrestling with a tricky and bouncing car.
"I think so," Wolff said, when asked by reporters whether Mexico was the best chance of avoiding a win blank for a campaign that has already seen Mercedes hand over the constructors' title to Red Bull.
"The good thing is that in our simulations we had that in a way on the radar, as being the best race, so that is good that the virtual world correlates with the real world.
"But the most important thing is that we really have the pace and slowly but surely we are going forward and learning the lessons for next year."
Wolff said he had never been confident of anything in Formula One, however.
"I'm annoyed about not being on pole, because it would have ticked a box, but then equally having Max with his top speed advantage behind us would have been a problem tomorrow," added the Austrian.
"And starting second and third can be advantageous and I hope we can stick our nose, or both noses, into turn one and then disappear into the distance. But definitely that's going to be difficult."
Hamilton has won twice previously in Mexico, including from third on the grid in 2019.
The Briton has won a race in every season since he entered the sport in 2007, a record unmatched by any other driver with his longevity. The remaining races after Mexico are Brazil and Abu Dhabi.
He was fastest in the first two phases but his first flying lap in the top-10 shootout was deleted, leaving the Briton with no time on the board and the pressure on to make no mistake.
"This is the best qualifying we've had all year, so it just shows that perseverance and never giving up is the way forward," said the winner of a record 103 races.
"The last lap wasn't good enough ... (but) I'm pretty happy with that position to start, it's a long way down to turn one."
Perez said he had an electrical issue throughout qualifying.
"I was pretty much blind through quali. I had no reference lap time, no information on brake balance sometimes, so it was just a mess," he explained.
"I nearly got knocked out in Q1 and Q2 (the first and second phases), so to be P4 is not the end of the world but I really believed that today we could have fought for pole position."
Carlos Sainz qualified fifth with Alfa Romeo's Valtteri Bottas splitting the Spaniard from Ferrari team mate Charles Leclerc.
Lando Norris will line up eighth for McLaren with Alpine's Fernando Alonso and Esteban Ocon completing the top 10.
Alpine are in a tight battle with McLaren for fourth overall.
