The 28-year-old Roman, ranked 34th, outgunned Norrie with 32 aces and 63 winners.
Berrettini, the 2021 Wimbledon finalist who helped Italy retain the Davis Cup last year, will face Dane Holger Rune in the next round.
In the women’s singles, Italy’s world number four Jasmine Paolini, who reached the finals of the French Open and Wimbledon last year, beat Chinese qualifier Wei Sijia 6-0, 6-4.
Back in the men’s, Lorenzo Musetti beat Matteo Arnaldi 7-6(7/4), 4-6, 7-6(7/5), 6-3 after four hours of combat in an all-Italian first-round clash.
Lorenzo Sonego is in the second round too thanks to a 6-4, 5-7, 7-5, 7-5 win over Swiss veteran Stan Wawrinka.
However, 21-year-old Luca Nardi lost his debut match in the Australian Open main draw to Canada’s Gabriel Diallo 6-7(1) 7-6(3) 5-7 6-1 6-2.
ANSA