On the run to the first corner, Verstappen edged Norris on to the grass on the inside of the straight and then braked too late to make the first corner, cutting the chicane.
That kept him in the lead, but the incident was immediately flagged by the stewards, hence Red Bull’s intervention.
Piastri had the best start of all in the top three, but had to back out of a challenge, and that let Leclerc attack him, and pass on the exit of Turn One.
Piastri came back at him, with a stunning move around the outside of Turn Four.
That gave Piastri a chance to attack Verstappen, but when he went long into Turn One, Leclerc again passed him, this time through Curva Grande, and Piastri backed out of an attempted pass back into the second chicane.
The natural order was finally established when Piastri passed the Ferrari at Turn One at the start of lap five.
By that time, Piastri was 3.5secs behind Norris, but he continued to fall back.
Leclerc had a lonely race to fourth, ahead of Mercedes’ George Russell, while Lewis Hamilton, in his first race for Ferrari at Monza, recovered well from his 10th place on the grid, after a five-place penalty, to take sixth.
Williams’ Alex Albon took seventh from Sauber’s Gabriel Bortoleto, Mercedes’ Kimi Antonelli and Racing Bulls’ Isack Hadjar.