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The world number one has dominated during the opening week in Melbourne and quickly eased past Giorgi, the Italian 30th seed, 6-2 6-3 on Rod Laver Arena.
Barty has dropped just eight games in the first three rounds at her home grand slam, where she is eyeing her third major title.
The Australian is on track to face Naomi Osaka in a blockbuster fourth-round clash, although the Japanese star was involved in a tight contest with Amanda Anisimova.
Giorgi made a nervous start and back-to-back double faults handed Barty a break of serve in the second game.
Barty rolled into a 4-1 lead before digging herself out of a 15-40 hole to hold for 5-2.
Speaking after her second-round win, Barty was wary of Giorgi's ability to hit players off the court, but 16 unforced errors were costly for the Italian in the first set.
Giorgi tidied up the errors to begin the second set, but a double fault handed Barty two more break-point chances in the sixth game.
The reigning Wimbledon champion took the second of those when Giorgi pulled a backhand well wide.
That break proved to be enough for Barty, who closed out a fourth win in as many meetings with Giorgi.