The Spaniard outgunned Red Bull's Verstappen to the delight of the Ferrari faithful with Charles Leclerc third in the other scarlet car.
George Russell finished fourth with Mercedes team-mate Lewis Hamilton only eighth on an underwhelming afternoon for the seven-time world champion.
Verstappen, who is bidding to become the first driver in history to win 10 consecutive races, trailed the Ferrari duo heading into the final runs at Monza's sun-cooked Temple of Speed.
But the double world champion appeared to have delivered the goods when he usurped both men with his last lap after he had made a rare mistake in his first run by kicking up gravel on the exit of Variante Della Roggia.
However, Sainz, who celebrated his 29th birthday on Friday and has been speedy all weekend here, sent the tifosi wild by pipping Verstappen in the closing seconds. Leclerc finished third, just 0.067 sec back in a nip-and-tuck qualifying session.
Both Ferrari men faced an investigation by the stewards after they were alleged to have driven too slowly on their warm-up laps in Q1.
The rule was updated on Saturday morning to avoid congestion and the possibility of accidents owing to the traffic.
But the stewards confirmed in the moments after Sainz's pole that neither the Spaniard nor Leclerc would face further action.
Hamilton endured a difficult day, 48 hours after signing a new deal to extend his stay on the grid for another two years.
The seven-time world champion is on a run of 35 races without a victory and he does not appear any closer to ending his barren streak.
The Briton managed to haul his Mercedes into Q3 after he complained he was lacking grip, before suggesting he had been impeded by Red Bull's Perez.
But he failed to make an impression at the very sharp end of the grid in Q3 after he qualified half-a-second behind Sainz and two tenths adrift of team-mate Russell.
Sergio Perez took fifth, while London-born Alex Albon, one of the standout performers of the season so far, impressed again.
While rookie team-mate Logan Sargeant was knocked out of Q2 in 15th, Albon not only progressed to the final phase but also saw off both McLarens, Hamilton and the Aston Martin of Fernando Alonso as he outperformed his modest Williams machinery to qualify sixth.
Oscar Piastri qualified seventh, two spots ahead of team-mate Lando Norris with Alonso 10th.