After Leclerc collided with the barriers for the second time of the weekend in Q3, the red flags were waved, bringing an end to an incident-packed session.
As a result, Fernando Alonso clinched second for Aston Martin, while Ferrari's Carlos Sainz completed the top three. Verstappen, meanwhile, was consigned to a lowly ninth-placed start and audibly aired his irritation over the team radio.
Leclerc will be forced to spar on the back foot in seventh after his loss of control.
Esteban Ocon and Valtteri Bottas sandwiched Verstappen, whose mistake at turns six and seven proved costly, to complete the top 10.
Conversely, Lewis Hamilton endured his worst-ever qualifying result on US soil. The superstar exited in Q2 and will start the main event in 13th.
Perez took pole position after Leclerc's crash
Verstappen and Leclerc embarked on their final runs under pressure, both having committed mistakes in the early stage of the session. The world champion ran wide to mar his attempt before Leclerc brushed the wall at turn 16.
And the pressure spilled over when Leclerc span on the entry to turn seven and backed his car into the wall just a day on from a similar slip-up in second practice.
Earlier in the day, the end of Q1 saw the timing tower take up a familiar picture, with the two Red Bulls and Ferraris trading blows. Verstappen eased through in first, followed by Sainz, while Perez and Leclerc made up the rest of the top four.
Magnussen delivered a superb effort to clinch fifth with his Haas, with Hamilton in sixth after sparing his blushes with his final flying lap. Russell, meanwhile, clung on to 11th after escaping the bottom five in dramatic fashion.
The big scalp from the first session was Aston Martin's Lance Stroll, although Yuki Tsunoda, Lando Norris, Oscar Piastri and Logan Sargeant shared his fate.
Verstappen emerged first for Q2 and wasted little time in hitting the ground running. Perez immediately found himself two-tenths slower while Fernando Alonso fought back from his sluggish start to move close to the benchmark.
Verstappen's bid for pole was denied by the late crash
Both Alpines and Haas drivers then embarked on good opening efforts, before Sainz and Leclerc finished their first laps. The former clocked a time just 0.038s adrift of Verstappen's, while the latter temporarily slotted into fifth.
With five minutes remaining, Perez was made to abort his flying lap after striking the wall on the entry to turn four, although he avoided lasting damage.
The track continued to change and Verstappen and Leclerc made use of the more forgiving surface by trading places at the top, the champion eventually taking first.
Hamilton, though, was eliminated in 13th while Russell scraped through in 10th. Alex Albon, Nico Hulkenberg, Zhou Guanyu and Nyck de Vries also crashed out.
The third and final session saw several drivers make mistakes while gunning for pole, and Leclerc's double spin ensured that Perez will front the grid on Sunday.
Sainz delivered a superb drive and will line up third on the grid
Hamilton KO after early blow
For much of Q1, Hamilton found himself languishing at the back of the pack and at real risk of elimination, showcasing Mercedes' struggles across the weekend.
He dived back into the pits early on after informing his team over the radio that his front wing had made contact with the barrier.
Replays then showed the seven-time world champion swerving slightly into the wall to avoid shunting Haas' Magnussen at turn 17.
And the afternoon took another turn for the worse in Q2, with Hamilton knocked out in 13th to chalk up his worst-ever qualifying session on US soil.
It has been a chastening weekend for McLaren, despite initial bursts of practice promise. Both drivers were eliminated in Q1, with Norris 16th and Piastri 19th.
Hamilton propelling himself into Q2 by the skin of his teeth delivered the fatal blow for Norris, who had briefly moved into 12th before the final sets of flying laps.
His rookie team-mate suffered a similar fate, having struggled to find his groove.
The only team not to appear in Q3 so far this year were Alfa Romeo, although the team brought a welcome end to this record thanks to the work of Bottas.
Bottas took seventh at the end of Q2 to reach the final shootout and at one stage almost appeared in touching distance of Leclerc before dropping back slightly.
Guanyu, on the other hand, was eliminated at the second hurdle in 14th.
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