The 19-year-old, ranked 26, underlined her huge potential with a confident performance to take out the German, 7-6 (7/5), 6-2 in a second-round match played in sweltering conditions.
Only last week Kasatkina held a match point before going down to French Open champion Garbine Muguruza in the second round at the Brisbane International.
While she continues her march, Kerber's form is a concern ahead of next week's opening Grand Slam of the year, having also lost to Ukraine's Elina Svitolina 6-4, 3-6, 6-3 in the quarter-finals of the Brisbane International last week.
Kerber, who had a breakthrough 2016, winning two Grand Slams on her way to becoming world number one, struggled to find any rhythm and her usually strong forehand was astray.
"I made too many mistakes and I was not actually feeling the ball, because the balls are flying here a little bit different than in Brisbane," Kerber said.
"So it was not so easy, but I will try to forget the match as soon as I can.
"I will go in the next few days to Melbourne, and I will try to get ready there, trying to get the positive energy from last year."
Asked about her emotions after her biggest win yet, Kasatkina said courtside: "Difficult to explain because I beat the number one in the world and it doesn't happen every day. I think I got some confidence."
Kasatkina will next play British world number 10 Johanna Konta, whose formidable serve troubled Australia's Daria Gavrilova in a 6-1, 6-3 win.
"I'm just happy I have accumulated a few matches already under my belt in the first few weeks of the season," Konta said.
It was a day of upsets in Sydney where temperatures sizzled around 36 Celsius (97 Fahrenheit), with defending champion Svetlana Kuznetsova and last year's finalist Dominika Cibulkova both knocked out in the second round.
World number nine Kuznetsova went out to Russian compatriot Anastasia Pavlyuchenkova 7-5, 6-3 while Canada's Eugenie Bouchard continued her return to form with a 6-4, 6-3 win over the sixth-ranked Cibulkova.
Former Wimbledon finalist Bouchard, who has now won consecutive matches at a tournament for the first time since August, stretched her lead over Cibulkova to 4-1 head-to-head and will face Pavlyuchenkova in the last eight.
"Any time you play one of the best players in the world it's like a standard of where you're at," Bouchard said.
"I have taken a couple of solid steps this week, but I'm far from where I want to be. Even though I won, to me, I could do a lot of things better."
World number 27 Pavlyuchenkova, who knocked out Australian number one Samantha Stosur in the first round, won in her first career meeting with Kuznetsova.
Ninth-seeded Italian Roberta Vinci was another seed to fall, losing 6-2, 6-3 to veteran Barbora Strycova of the Czech Republic.
Danish seventh seed Caroline Wozniacki ousted Yulia Putintseva 6-0, 7-5 and will next face Strycova.