A mistake from the Australian on his final run in Qualifying 1 saw him eliminated from the three-part session at the first hurdle for the first time in 2024.
Sainz stormed to top spot with pace in hand over the pack, heading a similarly impressive Max Verstappen with Lando Norris third.
Liam Lawson will start 12th, the Kiwi unlucky with the timing of a red flag, triggered by his RB team-mate, as it denied him a final flying lap in Qualifying 2, and a potential Q3 berth.
McLaren opted for a set of medium tyres for its two drivers at the start of Qualifying 1, as did Ferrari with its pair.
That saw Norris second fastest with his initial lap, a 1:17.203s which compared with the provisional pole time set by Verstappen on a 1:16.998s.
Those early times didn’t stand as the track quickly ramped up.
Yuki Tsunoda went third fastest, then Nico Hulkenberg second, the German quickly replaced there by Alpine’s Pierre Gasly.
It meant nobody was safe; the entire field, with seven minutes remaining, needed a second run.
Oscar Piastri started that comparatively early with a soft tyre run with five minutes remaining.
It was a subdued lap, rising him from 19th at the time to only 13th best with a 1:17.631s – which was subsequently deleted for track limits at Turn 12.
The Australian remained on track, completing a cool-down lap before attacking again.
However, it was sluggish, and at the end of the lap, he recorded a only 1:17.597s to rise to just 14th.
Perez was also in danger as he could do no better than 15th having sat 20th when he started his final flying lap.
As others improved, both the local favourite and Piastri were bundled backwards, the McLaren driver falling to 17th and Perez 18th to become two high-profile eliminations at the end of Q1.
At the chequered flag, Franco Colapinto was 16th for Williams with Esteban Ocon 19th and Zhou Guanyu 20th to complete the five out of the session.
While one McLaren missed the cut, Norris in the other topped the session from Carlos Sainz and Max Verstappen.
Liam Lawson also progressed with comparative ease, logging the 13th best time with a 1:17.380s.
The order remained especially fluid as Qualifying 2 began, with Pierre Gasly towards the top of the timesheets.
Norris sat at the very top with a 1:16.301s, three-tenths faster than Verstappen after their first runs.
Leclerc had his first lap deleted after he cut behind the apex kerb at Turn 2 leaving him without a time ahead of his second Q2 run.
He completed a second lap with two minutes remaining, managing a 1:16.641s that left him third fastest – fourth once Sainz flashed across the line soon after.
Inside the final minute, Lawson held 10th place, bundled back to 12th as the red flag was thrown for Yuki Tsunoda who’d crashed at Turn 12 – the right-hander entering the stadium.
Tsunoda was 11th fastest at the time, one spot ahead of Lawson, joining Fernando Alonso, Lance Stroll, and Valtteri Bottas on the sidelines.
It was a costly mistake from the Japanese driver after both RB drivers showed top 10 potential.
Instead, both Haas drivers progressed as did Alex Albon, the Williams driver taking full advantage of the lack of Piastri, Perez, and both RBs.
Tsunoda’s crash delayed the start of Q3, all 10 remaining drivers heading out soon after the pit exit did go green.
That saw Verstappen produce a 1:16.368s, a time six-tenths faster than what Norris could manage.
The McLaren driver sat second, which became third when Charles Leclerc elbowed his way between the two title rivals, and fourth when Sainz went faster than everyone else.
However, there was drama when Verstappen’s time was deleted for track limits at Turn 2 – he’d cut behind the apex kerb of the left-hander.
There was time for another run for the championship leader, who also had a set of new soft tyres at his disposal.
Mercedes ran slightly out of sequence to sit third and fourth after their initial runs.
Inside the final minute, both Charles Leclerc and Carlos Sainz both improved on their laps, the latter improving to a storming 1:15.946s.
Leclerc had climbed to second but was dropped to fourth after Verstappen and Norris completed their laps.
Verstappen’s lap was 0.225s slower than Sainz but good enough for second, with Norris a tenth further back in third.
Russell was fifth ahead of Hamilton, then Kevin Magnussen, Gasly, Albon, and Hulkenberg.
It was a hugely impressive lap from Verstappen, the Dutchman wrestling his Red Bull Racing onto the front row with a car that was clearly less impressive than the Ferrari or McLaren.
However, his title rival will start on the clear side of the track on Sunday, and in the slipstream of the pole-sitting Ferrari.
Mercedes had no answer, despite flashes of pace at times that suggested otherwise.
Haas enjoyed another positive qualifying session, though a mistake at Turn 12 for Hulkenberg was likely the difference between 10th and a spot closer to his team-mate in seventh.