Barty, who is aiming to end Australia's 44-year wait for a homegrown champion, had lost only three games in her first two matches and continued that dominant form with an early break of the 30th seed's serve.
Giorgi can be a tricky opponent if she is allowed to get into her stride and Barty was 40-0 down in the sixth game of the set as the Italian threatened to break back.
The Wimbledon champion saved all three break points, won the game with an ace and then proceeded to break Giorgi again to seal the opening set.
A break for 4-2 put Barty in charge of the second set and three games later she was bathing in an ovation from the centre court crowd having secured her place in the last 16 at Melbourne Park for the fourth straight year.
"I thought tonight was really clean, I looked after my service games really well," said Barty.
"I was able to keep the momentum going, make returns when it mattered most at the important moments, pretty good performance I think."
Barty had obviously given plenty of consideration to the idea that she might be playing American Anisimova, who she beat in the French Open semi-finals on her way to winning her first Grand Slam crown in 2019.
"It will be nice to play each other again in a big match," said Barty.
"It feels like it's a lifetime ago, but some of those memories are still really vivid. Without a doubt we will take that and use that experience, use those feelings and those emotions as best we can come Sunday."
