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.
Max Verstappen ended a long wait for a race victory as he came out on top at the Italian Grand Prix.
Reigning four-time Formula One champion Verstappen went into Sunday's race at Monza having not tasted victory since triumphing at Imola in May.
But the Dutchman completed the Italian double with a brilliant drive, finishing almost 20 seconds ahead of McLaren duo Lando Norris and Oscar Piastri.
Verstappen, who claimed pole position during Saturday's qualifying, had to hold off an early charge from Norris, who claimed he was shunted onto the grass by the Red Bull driver during a frantic start.
Norris managed to get first place on the next lap, yet two laps later, Verstappen regained the advantage, and one which he did not relinquish.
Indeed, 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.
Piastri eventually did as instructed, with Norris holding off the Australian to claim second and close the gap between them in the standings to 31 points.
Last year's Italian Grand Prix winner Charles Leclerc finished fourth on a frustrating day for Ferrari on home turf, two places ahead of Lewis Hamilton in sixth, with George Russell in fifth.
Alex Albon, Gabriel Bortoleto, Kimi Antonelli and Isack Hadjar rounded out the top 10 at Monza, where Fernando Alonso and Nico Hulkenberg failed to finish.
Data Debrief: Verstappen completes the Italian job
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.
Piastri may have endured a frustrating day, but he has now finished each of his past 44 races. That is the second-longest such run in F1 history, after Hamilton (48 between the 2018 British Grand Prix and 2020 Bahrain Grand Prix).
Top 10
1. Max Verstappen (Red Bull)
2. Lando Norris (McLaren)
3. Oscar Piastri (McLaren)
4. Charles Leclerc (Ferrari)
5. George Russell (Mercedes)
6. Lewis Hamilton (Ferrari)
7. Alex Albon (Williams)
8. Gabriel Bortoleto (Sauber)
9. Kimi Antonelli (Mercedes)
10. Isack Hadjar (Racing Bulls)
CHAMPIONSHIP STANDINGS
Drivers'
1. Oscar Piastri (McLaren) - 324
2. Lando Norris (McLaren) - 293
3. Max Verstappen (Red Bull) - 230
Constructors'
1. McLaren – 617
2. Ferrari - 280
3. Mercedes - 260
