After a difficult time through the practice sessions in Mexico City, where their SF-23 car appeared to be no match for the pace-setting Red Bull, the duo sprung a major surprise at the start of the Q3 qualifying segment.
Their cars suddenly came alive and it helped Leclerc and Sainz take the provisional top two slots on the grid – which were then secured as their main challengers were unable to find improvements in the final runs.
Max Verstappen will start third for Red Bull ahead of Daniel Ricciardo's AlphaTauri in fourth.
Sainz, who ended up 0.067 seconds behind Leclerc, said it was difficult to understand why their car was suddenly so good on one lap and then could not match that pace again.
"It was a very strange one," admitted Sainz. "Honestly, the whole weekend I've struggled to put a lap together, and the first lap that I put together was Q3 run one.
"Suddenly it was P1 at the time, and then Charles pipped me by half a tenth. But I just struggle to understand where suddenly we can find half a second and then go half a second slower in the next lap.
"It's very tricky with the tyres, and the feeling with the car is very strange around the circuit. But we managed to put a good lap when it counted. And it puts us in a good position for tomorrow."
Leclerc had come into the day playing down any talk of being able to repeat the pole position that he took at last weekend's United States Grand Prix. That is why he said the repeat top spot in qualifying was a shock.
Asked if he felt he had this potential in the car, Leclerc said: "Absolutely not.
"It's been two weekends in a row where we say that, so then people will start not believing us anymore. To be honest, I did not expect to be on pole position.
"Today, we thought we were lacking quite a bit after FP3. But for some reason, once we put everything together, it went well, [and with] the new tyres, we gained a lot.
"But I'm already focusing on tomorrow's race, because after many pole positions, now we need to convert it into a win tomorrow. And of course, it's going to be very difficult."
But while Leclerc is eager to deliver a triumph on Sunday, Sainz was cautious about Ferrari's potential over long runs.
"Clearly, we are not as strong in high fuel as we are in low fuel," he said. "I think our car benefits a lot from that new tyre, soft tyre peak at the rear.
"We're going to see how we can do tomorrow to keep those tyres alive and to keep that Red Bull behind, because having two cars in front is a good advantage."
