The Dutchman, who has won the event at the Autodromo Hermanos Rodriguez here in each of the last two years, made it around the track in 1:14.758 late on Saturday.
Ferrari drivers Charles Leclerc and Sebastian Vettel took the second and third spots, respectively, while Lewis Hamilton (Mercedes) will start Sunday's race in fourth position, reports Efe news.
Verstappen's Red Bull teammate, Alex Albon, secured the fifth spot, alongside Valtteri Bottas (Mercedes) in sixth. The McLaren team - Carlos Sainz and Lando Norris - will occupy the fourth row on the starting grid.
For Spain's Sainz, it will be a fifth consecutive top-seven start.
Daniil Kvyat and Pierre Gasly, both of Toro Rosso, completed the top 10.
Bottas suffered a major crash in the final qualifying round and while the Finn wasn't hurt, the extent of damage to his car remained to be determined.
The only Mexican driver currently competing in F1, Sergio "Checo" Perez, failed to reach Q3 and will start 11th on the grid.
Much expectation surrounds this year's Mexican Grand Prix because the 34-year-old Hamilton can clinch a third straight drivers' title and sixth championship overall on Sunday.
That would leave him just one shy of the record held by German racing great Michael Schumacher, who won seven drivers' titles between 1994 and 2004.
Hamilton leads the 2019 drivers' standings with 338 points, 64 more than teammate Bottas.
The British driver and his Mercedes car have been remarkably consistent throughout the year, with Hamilton not having been forced to retire from a single race and only once finishing outside of the top five through 17 races.
After the Mexico stop, the season will continue with two more races in the Americas in November: the US Grand Prix at the Circuit of the Americas in Austin, Texas, on November 3; and the Brazilian Grand Prix at the Jose Carlos Pace Autodrome in Sao Paulo's Interlagos neighbourhood on November 17.
The season will wrap up on December 1 with one final race at the Yas Marina Circuit in Abu Dhabi.
( With inputs from IANS )