The Aussie pair were cheered on by a hopeful home crowd at the Rod Laver Arena but made a poor start, falling a set behind in just 30 minutes thanks to a string of unforced errors on serve.
Errani and Vinci claimed an early break in the second set and looked to be coasting towards victory, but a spirited fightback kept the Aussies alive in the contest.
Barty in particular started to find her range from the baseline and thundered home a backhand winner to level the match at a set apiece.
Dellacqua and Barty had all the momentum and broke in the opening game of set three but faded away just when it mattered most.
Errani and Vinci used their edge in experience to break back instantly before romping home in the final set to claim their third Grand Slam title in the last 12 months.