From there, the commanding Dutchman never looked back to better the mark he shared with Sebastian Vettel and become the first driver in F1 to reach double figures for straight victories.
Sergio Perez finished second in the other Red Bull, while Sainz held off team-mate Charles Leclerc in a tantalising late battle between the Ferrari drivers to take the final spot on the podium.
George Russell finished fifth with Lewis Hamilton, who served a five-second penalty for colliding with McLaren's Oscar Piastri, sixth.
“That is history,” said Red Bull team principal Christian Horner to his superstar driver. “Unbelievable.”
Verstappen's 12th win from the 14 rounds so far moves him 145 points clear in the championship.
Unbeaten since the Azerbaijan Grand Prix on April 30, there remains an outside chance the 25-year-old could be crowned champion of the world for a third time as early as the Japanese Grand Prix in three weeks with half-a-dozen rounds still remaining.
Sainz lit up Ferrari's home track by taking pole position and kept the dream alive of a victory in front of the Italian team's 80,000-strong crowd by holding off Verstappen on the 500-metre drag to the opening Variante del Rettifilo.
Verstappen was the filling in a Ferrari sandwich with Leclerc maintaining third spot ahead of Mercedes' Russell and Perez. Hamilton started eighth but dropped one position on the first lap.
Such has been the superiority of Verstappen's Red Bull machine this year, Sainz was expected to be easy prey for the all-conquering Dutchman. But to Verstappen's surprise, Sainz was not prepared to make life easy for the double world champion.
On lap six, Verstappen was handed his first opportunity, drawing alongside Sainz on the 220mph run to the first chicane, only for the Spaniard to slam the door in his face.
“That was naughty,” said Verstappen. Three laps later, Verstappen was back on the intercom. “They have a lot of top speed, for f*** sake,” he said.
Further back and Russell's mirrors were occupied by the other Red Bull of Perez. Asked to manage his rubber, the Englishman replied: “I don't know if you can see, but I have got a car right up my a***”.
Up front and Verstappen sensed another chance to take the lead on lap 15. A defensive Sainz locked up at the Variante del Rettifilo, handing Verstappen the exit speed on the 200mph charge to the Variante della Roggia.
This racing 🥵
Max Verstappen takes the lead in Monza! 💥 pic.twitter.com/ojqcX84e5m
— Sky Sports F1 (@SkySportsF1) September 3, 2023
The Red Bull and Ferrari machines were separated by mere centimetres as they went toe-to-toe into the second chicane before Verstappen, benefiting from the inside line, emerged in the lead.
Remarkably, Sainz's 14 laps in the lead was the highest in any event this season by a non-Red Bull driver. The team from Milton Keynes could yet become the first team to go an entire campaign unbeaten with eight races to run.
On lap 16, Perez moved up to fourth with Russell - struggling for top-line speed in his Mercedes - unable to keep the Red Bull behind.
With Verstappen cruising imperiously to victory, Perez moved up third after seeing off Leclerc. The Mexican set about passing Sainz, and, after a number of failed attempts, he finally blasted past the Ferrari with five laps remaining to ensure a one-two for Red Bull.
After emerging from his tyre stop in 10th, Hamilton moved ahead of Fernando Alonso before banging wheels with Piastri in the battle for eighth. Hamilton was hit with a penalty for the incident at the Variante della Roggia as Piastri pitted for a new front wing.
“He just turned across me under braking,” bemoaned the Australian rookie.
Undeterred by his sanction, Hamilton then raced ahead of Lando Norris before moving past Alex Albon's Williams to take sixth, finishing 7.4 seconds clear to ensure his penalty had no impact on his result. Albon finished seventh ahead of Norris, with Alonso ninth.