The winner in Mexico has come from third on the grid in three of the last four races.
Norris said: “I am pretty happy with third, honestly. I feel like I got to the limit of the car quite quickly, which made us look quite good but I struggled to get any more out of it.
“None of us have done proper long runs on the tyres we’re going to be on tomorrow but Ferrari have been very quick in qualifying and on the long runs recently so it’s going to be tough.”
Both Norris and Verstappen faced more pressure than normal going into the final laps because neither had a good lap time on the board.
Verstappen’s first lap was deleted for exceeding track limits and Norris’ was just slow.
Verstappen, who lost nearly all of Friday with an engine problem, said: “Yesterday I did basically no laps, so I was already under a lot of pressure and then that added a little more pressure.
“I’m very happy to be on the front row, I didn’t think that would be possible.”
Sainz said: “Great couple of laps. A lot of times around Mexico you always have the feeling like you cannot put a lap together and it is extremely difficult with how much sliding there is. But my two laps were almost identical, almost perfect.
“Since Austin, we have done especially on my side a step up, also in qualifying trying to find something different with the out-lap and the tyre preparation. Looking forward to finishing the job tomorrow but I will take pole position. Very happy.”
Norris has no support from his team-mate Oscar Piastri, who was knocked out in the first session for the second race in a row.
McLaren did their first runs on medium tyres in the first session to try to save softs for later but it seems to have harpooned Piastri.
The Australian said: “The medium I didn’t have much confidence on, the first soft lap I was going well and then I just went wide at Turn 12. We tried to go again but I had zero grip because the tyres were too hot. Disappointing.
“The car is quick. Just a shame I have to start from the back again. Ironically, it’s the same place Lando started last year and he did have a good race, so all is not lost.”
Verstappen’s team-mate Sergio Perez also had another difficult session, 0.8secs slower than Verstappen in Q1 and knocked out in 18th place.
“Into the low speed, I cannot brake, I cannot attack the car,” Perez said. “I just start sliding. That is my main issue at the moment and here it showed even more.
“Every time I try to attack, it just starts locking up. There are four races to go and we have to get on top of it as a team.”
Russell was positively surprised to be as high as fifth after crashing in second practice on Friday, the fourth incident for a Mercedes driver in four days of on-track action. That meant he is running an older-specification car while Lewis Hamilton has the upgrade introduced in Austin.
“Really happy with the recovery,” he said. “We are still on the old bits from 12 races ago. My lap felt really strong, super-happy with it.
“Checo and Piastri are out of position. P5 is probably is the best we could have hoped for. The three teams in front have got a bit of a battle on their hands so maybe the race will come towards us.”
Fernando Alonso qualified 13th for Aston Martin on the weekend on which he is celebrating his 400th grand prix, but said he felt he could have been in the top 10 had it not been for a red flag that truncated second qualifying when Yuki Tsunoda crashed his RB coming into the stadium section.
“There was more to come,” Alonso said. “I was happily surprised by the car in qualifying. It felt much better and I could attack with confidence.
“The lap with red flag I was 0.2secs up and maybe P9 or P10 was possible. Happy with the car and maybe this gives us a trend to come back in the race.”
