The Dutchman was held back by pole-winner Carlos Sainz’s Ferrari for 14 laps but his pressure paid off when an error from the Spaniard gave him his chance.
Sainz locked his brakes into the first chicane and that allowed Verstappen to pass the Ferrari into the second chicane at Monza.
Sainz, after forcefully holding on to second place from team-mate Charles Leclerc, was left to fend off Verstappen’s team-mate Sergio Perez for second place.
After many laps of defence, Sainz finally lost the position with nine laps to go and then set about fighting hard again to keep Leclerc behind for the final podium place.
It was frantic at times as Sainz hung on with worn tyres, and eventually the Spaniard pleaded to his team to let him “bring it home”. Leclerc was told: “Race until the end, no risk.”
Sainz clung on with some desperate late braking moves into the first chicane, and eventually the fight was settled at the start of the final lap.
Leclerc sold the dummy to Sainz at the first chicane but the Spaniard moved to defend and Leclerc had to lock all his brakes and cut the chicane to avoid his partner. Leclerc crossed the line just 0.1secs behind.
Mercedes’ George Russell drove a steady race to take fifth, overcoming a five-second penalty for leaving the track when passing Esteban Ocon after leaving the pits.
Lewis Hamilton impressed on an inverted strategy, starting on the hard tyre and switching to the medium, to pass the McLarens and Alex Albon’s Williams to take sixth.
Hamilton also earned a five-second penalty for colliding with McLaren’s Oscar Piastri when passing him at the second chicane but had enough of a margin to keep the place.
Albon clung on ahead of McLaren’s Lando Norris, while Fernando Alonso had his most anonymous race of the season to take ninth in the Aston Martin ahead of Alfa Romeo’s Valtteri Bottas.
Piastri had to pit to repair damage after the Hamilton incident and finished 12th behind Liam Lawson’s Alpha Tauri.
Verstappen’s 10th win in a row moves him clear of Sebastian Vettel’s total of nine, also achieved in a Red Bull, in the 2013 season.
Asked about his achievement, Verstappen said: “I never would have believed that was possible but we had to work for it today and that made it definitely a lot more fun.
“We had good pace, I think we were good on the tyres but [Ferrari] had a lot of top speed, it was so hard to get close and get a move on into Turn One so I had to force him into a mistake.”
Red Bull have now won all 14 races so far this season.
