Verstappen has now won three of the last four editions of the Italian Grand Prix, having also claimed his first pole position at the event this weekend.
This is just the third time in the past 10 editions of the race that the driver starting on pole has gone on to win it.
The drama late on in the race came from McLaren, with championship leader Piastri told to allow team-mate Norris to pass after the latter had a slow pit stop.