On a manic day for the seeded players, the 19-year-old Kasatkina won 7-6(5) 6-2 against two-time grand slam Kerber, who also in the quarter-finals in Brisbane last week.
"It's difficult to explain really. I beat the number one in the world and it doesn't happen every day," Kasatkina, ranked 26 in the world, said in a courtside interview.
"I think I will get some confidence," she said referring to the year's first grand slam, starting on Monday in Melbourne, where Kerber would defend her women's title.
Anastasia Pavlyuchenkova earlier won an all-Russian battle against Svetlana Kuznetsova to oust the defending champion in straight sets.
Pavlyuchenkova beat world number nine Kuznetsova 7-5 6-3 to set up a quarter-final clash against Canadian Eugenie Bouchard, who caused another upset by defeating number three seed Dominika Cibulkova.
Ninth seed Italian Robert Vinci also fell to Czech Barbora Strycova 6-2 6-3 but former world number one Caroline Wozniacki bucked the trend with a 6-0 7-5 win over Kazakh Yulia Putintseva.
Pavlyuchenkova came into the match having lost five of the last six meetings against Kuznetsova and twice fell back in the opening set.
The 31-year-old double grand slam winner was serving for the set at 5-4 before Pavlyuchenkova reeled off the last three games to bag the set.
"I'm really happy, especially because she's not only defending champion but my fellow (countrywoman) and she's top 10 and she's had a really incredible year last year," Pavlyuchenkova said.
"I think I did everything well. I wasn't serving as well as I did yesterday; I was a little upset with that, but I'm so happy that even with a lower first serve percentage, that I was able to win the match in two sets."
Next up for the Russian will be former Wimbledon finalist Bouchard who completed her fourth consecutive hard-court win against world number six Cibulkova with a 6-4 6-3 victory.
It will be the first WTA quarter-final appearance for the Canadian in 10 months since Kuala Lumpur, where she lost in the final of the Malaysian Open.
"Any time you play one of the best players in the world... it's like a standard of where you're at," Bouchard said after taking her head-to-head record over Cibulkova to 4-1.
