The 18-year-old, preparing for only his sixth Grand Prix weekend, lapped with a best time of one minute 26.482 seconds to pip McLaren's championship leader Oscar Piastri by 0.045 seconds.
Australian Piastri, winner of four of the last five races, lapped the Imola circuit with a fastest time of one minute 16.545 seconds on the softest tyre compound with Norris 0.032 slower on a sunny afternoon.
Dutch driver Verstappen won his fourth successive title with Red Bull in Las Vegas last month.
Days after the Red Bull driver and partner Kelly Piquet welcomed daughter Lily, his first child, the four-times champion set a blistering lap of one minute 26.204 seconds around the Hard Rock Stadium.
Lando Norris lucked in to win a rain-hit and crash-strewn Miami Grand Prix sprint race in a McLaren one-two on Saturday.
The win from fourth on the grid was Australian Oscar Piastri's third in a row, after Bahrain and Saudi Arabia, and fourth of the season. McLaren have so far been beaten only once.
Red Bull's triple World champion Max Verstappen claimed pole position on Saturday for the Miami Grand Prix, to start from the front of the grid for the sixth straight race this season.
Lando Norris capitalised on a bit of good fortune to win the Miami Grand Prix on Sunday
It is doubtful there has been a more popular winner of a Formula One race in recent years than McLaren's Lando Norris, who was celebrated by everyone from Max Verstappen to Donald Trump following his victory at the Miami Grand Prix on Sunday.
Fernando Alonso will start the Miami Grand Prix on the front row alongside pole sitter Sergio Perez, providing Aston Martin the chance for a win, believes team principal Mike Krack.
Formula One championship leader Charles Leclerc took pole position for the inaugural Miami Grand Prix ahead of Ferrari team mate Carlos Sainz in a front row lockout in qualifying on Saturday.
Max Verstappen won the Miami Grand Prix from ninth on the starting grid with a masterful display of tyre management on Sunday.
Seven-times Formula One world champion Lewis Hamilton will race in Sunday's inaugural Miami Grand Prix after Formula One swerved a showdown with the Mercedes driver over their ban on piercings and jewellery.