The power-hitting 27-year-old, a virtual unknown before the tournament started, battled back from two sets down to upset the Canadian 3-6, 1-6, 6-3, 6-3, 6-4 on Margaret Court Arena.
It continued his giant-killing run after blitzing eighth seed Diego Schwartzmann in round three, setting up a quarter-final clash with either world number three Dominic Thiem or Grigor Dimitrov.
“It was really tough in the beginning to play against him. He played really fast and it took me two sets to find a way how to play,” he said.
“In the end I got into the rhythm in the third and fifth. I’m feeling good, but tired. I put everything into this match.”
Karatsev, ranked 114, is the first Grand Slam debutant to reach the quarter-finals at a major since Romanian Alex Radulescu at Wimbledon in 1996 and only the seventh in the Open era.
He is the first qualifier to achieve the feat since Australia’s Bernard Tomic at Wimbledon in 2011 and only the third ever at the Australian Open after Bob Giltinan in 1977 and Goran Ivanisevic in 1989.
The bearded Karatsev has been on the verge of playing a Grand Slam for years, but on nine previous attempts the injury-dogged Russian fell in qualifying.
He was part of the victorious Russian ATP Cup team this month along with Daniil Medvedev and Andrey Rublev, who play their fourth-round matches on Monday.