Croatian 19th seed Donna Vekic also crumbled to lower-ranked opposition when she lost 7-5, 6-3 to Poland's Iga Swiatek, who is returning from a stress fracture in her foot.
Kerber, who won the first of her three slam titles here in 2016, is the only former champion left in the women's draw.
Estonia's Anett Kontaveit thrashed Swiss sixth seed Belinda Bencic 6-0 6-1, as the seeds continue to tumble.
"It's just a tournament, and I'm sure that for you guys (media) it's a little bit of shock when the top-10 players are losing, but it's life and we can not be 100 percent every day", she said. "I served quite well and I was aggressive and I was doing the things I wanted to do really well", Kontaveit said in a courtside interview.
World No 2 Karolina Pliskova joined the list of seeds to exit the Australian Open at the third round after a straight-sets defeat to Russian Anastasia Pavlyuchenkova.
Giorgi struck an impressive 49 winners to Kerber's 15 but the 28-year-old was undone by 65 unforced errors.
This seemed another big chance for the Czech, arguably the best player on the WTA Tour over the past three or four years, to win a first grand slam title.
"I didn't check the statistics yet, but I think I can serve much better". "And to beat Karolina for the first time, it's awesome".
Fourth seed Halep - runner-up in Melbourne two years ago - needed one hour, 18 minutes to progress to the fourth round.
Twice Grand Slam champion Halep, 28, will next meet the victor of the third-round match between Belgian No. 16 seed Elise Mertens and American Catherine Bellis.
Pavlyuchenkova had a 4-1 lead in the first set and a 2-0 lead in the second before being taken to tiebreaks but won the key points to clinch victory in 2hr 25min. However, she managed to keep her run alive by reeling off the next six games in succession.
Three-time major victor Angelique Kerber bucked the trend by beating Camila Giorgi 6-2, 6-7 (4), 6-3 on Margaret Court Arena.
World number one Rafael Nadal and Wimbledon champion Simona Halep dodged an exodus of seeded players as the shocks kept rolling at the Australian Open on Saturday.