Verstappen had looked a certainty for pole since the start of the weekend but in the end his margin was perhaps smaller than expected.
Perez was just 0.066 seconds adrift of the three-time champion, who had been half a second clear of the field on this same circuit last September.
Red Bull, though, were in a league of their own – Norris was 0.292secs off the pace in third, and himself a comfortable 0.193secs ahead of Sainz.
Verstappen said he felt it had not been this greatest lap, adding: “It was quite close at the end. This track is very sensitive with the tyre with the Tarmac being aggressive, and when you really want to go to the limit, it doesn’t always work out.
“It is good to be on pole, a good starting position for tomorrow, and tomorrow is what counts.”
Perez said: “It was really close with Max. It felt like a good lap. It was quite tricky there, especially closing the laps it was easy to lose a couple of 10ths in the last sector.
“We have been really close all weekend and when you are in that, little margins… anything can make a difference.
“I didn’t have a great exit (from the chicane) opening the lap; that could have been different. Our long-run pace was not that strong this morning but we have worked quite a bit and hopefully we will be strong.”
Norris was pleased with third, saying McLaren’s “hard work was paying off” in trying to close the gap to Red Bull.
Sainz was 0.485secs from pole, a step forward for Ferrari compared to last year but their least impressive qualifying performance of the year.
And Leclerc, while only 0.104secs off the Spaniard, was perplexed as to where his pace has gone this season.
Leclerc has been the faster Ferrari driver on balance through their time as team-mates and he has been re-signed for next season alongside Lewis Hamilton while Sainz is looking for a drive.
But Sainz has been more impressive this season and Leclerc said after qualifying: “That’s the best I can do. Honestly, I don’t get it.”
It was an encouraging day for Alonso, whose Aston Martin has major floor upgrades this weekend and the veteran Spaniard put them to good effect.
Second fastest in the first session, Alonso slipped back as qualifying progressed and others found their feet.
He was seventh after his first run in the final top 10 shoot-out and was encouraged by his engineer to try to find the extra 0.15secs that separated him from a place in the top four at the time.
Alonso replied saying: “I don’t know what to do to go faster; it felt like a good lap.” But he found almost exactly that time to move up and split the Ferraris and McLarens.
The 0.569secs that separated Hamilton from pole was seen as progress at Mercedes.
Hamilton said: “It’s been a night and day different weekend so far in terms of how comfortable I felt in the car, we did a really good job of analysis back at the factory to try to understand how we can get the car in a sweeter spot.
“The car has a been much nicer to drive this weekend and particularly at a track like this where you need a nice balance, this is the nicest it’s been for three years.
“Last year we were a second off, 0.7secs today.”