Fourth seed Sinner continued to underline his title contender credentials as he came through a tough test against Russia's Khachanov.
Sinner was far from his best but managed to survive nine break points and hit 46 winners to come out on top after two hours and 34 minutes on Margaret Court Arena.
"Usually when we play it's a tough match, he's [Khachanov] an incredible player, I tried to stay focused, mentally and physically," Sinner said.
"Every match has its own story. Today I won so I'm very happy. We have quite a similar game style, so it's a kind of ping-pong. I tried to mix it up a bit today."
The 22-year-old, who is yet to drop a set in the tournament, is on course to meet Djokovic in the semi-finals.
Sinner won four titles in 2023 and ended it on a high by leading Italy to a first Davis Cup title for 47 years.
He defeated Djokovic twice in the space of 10 days in 2023 - in the ATP Finals round-robin and Davis Cup semi-finals.
However, Djokovic did claim a dominant victory over Sinner in the final in Turin to win a record seventh ATP Finals title.
Up next for Djokovic is Fritz, who beat Greek seventh seed Tsitsipas 7-6 (7-2) 5-7 6-3 6-3 to reach his first Australian Open quarter-final.
Djokovic has won all eight of their previous matches, including a straight-set victory at the 2023 US Open.
When asked in his news conference about an answer Djokovic gave about the possibility of playing Fritz, the American said: "If I beat someone eight times in a row, I'd be pretty confident playing them, too. I can't really fault him for that.
"I think that I have a lot more level to bring than I've previously brought against him. Hopefully I can play another match like today."
Sinner's next opponent Rublev battled cramp as he closed out a 6-4 6-7 (5-7) 6-7 (4-7) 6-3 6-0 win over 10th seed De Minaur.
With a partisan crowd against him, Rublev showed visible signs of frustration as De Minaur wrapped up a third-set tie-break to lead by two sets to one.
But he composed himself to force a decider which he raced through in 30 minutes.
"When I was losing two sets to one down, I told myself you're going to die today but you will do everything," Rublev said.
"Then somehow I started to play better and better and I found more energy and I was able to win.
"I was just trying to push myself. Don't cry, don't start to feel sorry to yourself, keep fighting and then we'll see what's going to happen."
ncG1vNJzZmivp6x7o67CZ5qopV%2BovbC%2B02irnqaensBwgpdpa2ptZWU%3D