Leclerc will be demoted 10 places following an engine penalty, promoting world champion Max Verstappen to the front row for Sunday's race at the Circuit of the Americas.
Sergio Perez qualified fourth in the other Red Bull, but drops back to ninth for exceeding his number of allocated engine parts.
Lewis Hamilton finished fifth but will take advantage of the penalties served by Leclerc and Perez to occupy third position on the grid, with Mercedes team-mate George Russell one spot back.
Verstappen's build-up to what should be his championship party in Austin, Texas has been dominated by talk of his Red Bull team's breach of last year's budget cap.
Team principal Christian Horner went on the attack on Saturday morning, labelling McLaren boss Zak Brown's claims of cheating as "shocking and appalling".
Ahead of practice on Saturday, a group of spectators booed Verstappen and directed a chant of "cheater" at the Dutchman as he was presented on stage during a fans' event.
It was then announced that Red Bull co-owner Dietrich Mateschitz had died, aged 78, following a long-term illness.
"It has been hard news, for everyone to take," said Verstappen, 25.
"What he has meant for Red Bull, but also the sport and especially what he has done for me in terms of my career so far and in general my life. Without him I would not be sitting here today and I would not have had the success I have had.
"It has been a very tough day. Unfortunately we missed out on pole but there is still a race ahead and we are going to try and make him proud tomorrow."
Verstappen has been the standout star of this season, and a win in the Lone Star state will see him equal a record shared by Michael Schumacher and Sebastian Vettel of 13 victories in a season.
And although Sainz lines up ahead of him on the grid, the two-time world champion will be the favourite to capture victory, with Red Bull unbeaten in their last seven outings. Bar a miserable performance here on Sunday, the team from Milton Keynes will also capture their first constructors' championship since 2013.
Mercedes, the sport's once dominant team, are trialling a new front and rear wing and revised floor at the 19th round of 22, with Hamilton still seeking his first victory of the season.
But the seven-time world champion is running out of time to ensure his record of winning at least one race in each year he has competed in remains intact, with just four rounds remaining.
Grid sanctions for Leclerc and Perez will at least put Hamilton on Verstappen's gearbox for the start of a race he has won five times previously. But the qualifying gap of almost six tenths to the front suggests he will not be in a position to challenge.
Elsewhere, Lando Norris qualified eighth. His McLaren team-mate Daniel Ricciardo, without a drive for next season, fell at the first hurdle. He will start 17th on Sunday.