Sainz lapped Monza's "Temple of Speed" with a fastest time of 01:20.294, 0.013 quicker than Verstappen's final flying lap with Ferrari's Charles Leclerc qualifying third.
Just 0.067 of a second separated the top three drivers on a sunny afternoon at Monza with the Ferrari 'tifosi', who have had little to cheer about this season, roaring on the red cars as they took the battle to dominant Red Bull.
The pole was Ferrari's third of a season in which Red Bull have won all 13 races so far but Sainz's first since Austin, Texas, last October.
The final session took place with a stewards' enquiry hanging over the Ferrari pair for going too slowly in the first phase but that threat dropped away as the crowd went wild and officials decided to take no further action.
Sainz said he felt goosebumps as he crossed the final line and soaked up the reaction on his slowing down lap after an intense session.
"It's incredible. Everywhere we go it's just noise, support and encouragement and it's the best feeling you can have as a driver," said the Spaniard.
"Tomorrow I will give it everything to hold on to that P1. A good start, a good first stint and see if we can battle Max. Normally in the long runs he is quicker but I am going to give it all."
Verstappen said he was happy to be second, for a change.
"Of course tomorrow we’ll try to win the race. Normally we have a quicker race car, but let’s just enjoy today and then we’ll focus on tomorrow," said the Dutch driver.
George Russell will start fourth for Mercedes with Verstappen's team-mate and closest rival Sergio Perez fifth.
Alex Albon qualified sixth for Williams, ahead of McLaren's Oscar Piastri, Mercedes' seven times world champion Lewis Hamilton and McLaren's Lando Norris.
Verstappen had been quickest in the first two phases of qualifying, after Sainz was fastest in practice, but could not do it a third time.
The Ferraris were Red Bull's closest rivals in the second stage, a roar from the crowd greeting first Sainz going fastest and then Leclerc before Verstappen brought them back to reality.
Alpine's Pierre Gasly, a surprise winner at Monza with AlphaTauri in 2020, and team-mate Esteban Ocon both failed to progress beyond the first phase with the latter running wide at turn 10.
Lance Stroll's underwhelming form for Aston Martin continued, with the Canadian team owner's son qualifying last of all while team-mate Fernando Alonso secured 10th place on the grid.
Alfa Romeo's Guanyu Zhou and Haas's Kevin Magnussen also went out at the first hurdle in 16th and 19th places respectively.