Polesitter Sainz launched strongly to maintain the lead into the first Monza chicane and he then repeatedly defended well against front-row rival Verstappen during their early DRS battles down the main straight.
But on lap 15 of a shortened 51, Sainz locked up during the big Turn 1 braking zone to compromise his apex and the tighter line then delayed his corner exit to allow Verstappen to challenge under power.
The Red Bull RB19 driver held his line around the outside of Curva Grande before cementing first place into the second chicane on his way to a record-breaking 10th consecutive GP victory.
Verstappen reckoned he forced Sainz into this decisive mistake. He said: “We had good space. I think we were good on the tyres. But they had a lot of top speed.
“It was so hard to get close and get a move on into Turn 1. So, I had to force them into a mistake.
“Luckily, it came at some point where he locked up, and then I had better traction, of course, out of Turn 2 and basically from there onwards, we could again do our own race.”
Verstappen, who radioed on lap four to say he could see Sainz was already struggling to manage his rear Pirellis, eventually headed a Red Bull 1-2 over Sergio Perez by 6.064 seconds.
The defending two-time champion added: “I was just trying to stay patient.
“It was still a very long race. I could see them struggling a lot with the rear tyres. So, I just had to pick my moment.”
Sainz would pip Ferrari team-mate Charles Leclerc by 0.18s to claim the final spot on the podium, the two SF-23 drivers locking up repeatedly in a late, hotly contested dice.
Discussing Verstappen’s attempts at passing the Spaniard early on, Red Bull team principal Christian Horner told Sky Sports: “Carlos was defending like his life depended on it.
“There were a few comments raised. Carlos was very robust. He was a little late at times. He moved a bit.
“Look, he’s driving a Ferrari at Monza. He’s going to defend for his life. We kind of expected it. It was on the limit; it was great racing.
“[Verstappen said he] could see Carlos was moving around a bit with his rear tyres.
“I think he knew that if he kept it cool, that they were very vulnerable.”