Davis, who won her maiden title in Auckland in 2017, came through two qualifiers before storming into the final and won the trophy without dropping a set.
Cocciaretto had downed former Hobart International and Australian Open champion Sofia Kenin in three sets to reach the final.
With nothing to separate the two in the opening set, Davis breezed through the tiebreak without dropping a point before breaking early in the second to beat her younger opponent.
The American, who faces Danka Kovinic in the Australian Open first round, became the fourth qualifier to win the title in Hobart after Germany's Mona Barthel, Spaniard Garbine Muguruza and Belgian Elise Mertens.
In the Adelaide tune-up tournament, Belinda Bencic defeated Daria Kasatkina in the final after both players received walkovers in the semis.
