Pliskova downed the 27th seeded Italian 6-4, 3-6, 6-2 after a 131 minute arm wrestle to set up a fourth round meeting with Spanish 18th seed Garbine Muguruza.
Former world number one Pliskova took the first set at a canter and appeared to be cruising until Giorgi lifted in the second and forced a decider.
The Czech took a decisive break early in the final set after a marathon game that went for 13 minutes and went to deuce five times.
"I had trouble sometimes but I just stayed calm even though I lost the second set. I had my chances but that's tennis," she said.
"I was very positive in the third set and I'm very happy to be through."
She has made the quarter-finals in her last two appearances at Melbourne Park and entered this year's tournament on a high after winning the Brisbane International warm-up.
The 26-year-old has been a regular in the second week of Grand Slams in recent years, reaching the quarters or better six times since late 2016, but is still searching for a breakthrough win.
She has a 7-2 winning record over two-time Grand Slam champion Muguruza, including four straight sets victories on hard courts.
But even if she gets past the Spaniard she is in a tough section of the draw that pits her against either world number one Simona Halep or 23-time major winner Serena Williams in the last eight.