The Red Bull driver finished two-tenths of a second clear of the seven-time champion with a lap of one minute 32.910s, casting adrift Hamilton who is a four-time winner at Austin's Circuit of the Americas.
It was a remarkable performance from Red Bull because following the first practice session it appeared as if Mercedes' stranglehold on this event - with five wins in the last six races, would continue following a one-two, with Verstappen almost a second adrift.
That sparked talk about the rear suspension on the car which lowers the rear wing and diffuser assembly, eliminating the rake and drastically reducing drag.
But Red Bull slowly clawed themselves back into the fight, making significant setup changes overnight to suggest they had the edge over one lap after FP3, in addition to impressing on the long runs in second practice.
After the first runs in Q1, Bottas held a slender edge over Hamilton by 0.089s as the Mercedes duo were first out on track.
But Verstappen usurped the Finn to claim provisional pole by 0.267s only to find himself remarkably overthrown by Perez by 0.019s.
Come the second run, Hamilton and Bottas were again first on track, and this time it was Hamilton who improved to take provisional pole, only for Verstappen to have the last word, with Perez forced to settle for third and Bottas fourth.
The Finn, however, will serve a five-place grid penalty for the sixth change of his internal combustion engine, dropping him to ninth.
In front of remarkable crowds at the circuit, baking under 30-degree temperatures, the first session saw Leclerc lead the way ahead of Verstappen and Perez, with Hamilton and Bottas a lowly eighth and ninth respectively.
The Russian driver was also involved in two incidents in Q1 with both Aston Martin drivers in Sebastian Vettel and Stroll but escaped punishment from the race stewards after two quick investigations.
In Q2, led by Verstappen by three-tenths of a second over Hamilton, Esteban Ocon failed to make it into the top-10 shoot-out and will start 11th despite being given a tow at one stage by Alpine team-mate Fernando Alonso.
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