Cocciaretto, ranked 51st in the world, represented a potentially tricky first test for Osaka with the Italian coming into Miami having won the WTA 125 event in Charleston last week.
But the step up in class proved too much as Osaka showed flashes of the form that carried her to four Grand Slam crowns, breaking Cocciaretto at the first opportunity while never allowing her opponent a break chance in the opening set.
Osaka only needed one break in the second as well to get the job done, closing out the contest with an ace on her second match point.
The Japanese player next faces Ukrainian 15th seed Elina Svitolina, who is less than year into her return from maternity leave.
"I was watching her last year and I was admiring all her runs in Wimbledon," said Osaka of Svitolina's run to the semi-finals at Wimbledon. "It's going to be a really incredible honour to play against her."
Elsewhere, In an all-American first-round match-up, qualifier Katie Volynets upset compatriot and former Australian Open champion Sofia Kenin 6-2, 4-6, 6-3 while Croatia's Donna Vekic was a 6-4, 2-6, 6-2 winner against big-hitting Czech Karolina Pliskova and Sloane Stephens beat Angelique Kerber.
