The local hope fought back from losing the first set to snag a two-sets-to-one lead at Rod Laver Arena on Sunday and appeared destined to kick on as a frustrated and emotional Rublev waged a verbal war on himself.
But a brilliant Rublev came home with a wet sail to level proceedings, then put the foot down in the fifth set as de Minaur crumbled to win 6-4 6-7 (5-7) 6-7 (4-7) 6-3 6-0.
Alex de Minaur had his moments before going down to defeat against Andrey Rublev. (Lukas Coch/AAP PHOTOS)
There are no Australians left in either singles after de Minaur's third consecutive fourth-round exit at his home slam.
After prevailing in the longest match of his career (four hours and 14 minutes), Rublev will face world No.4 Jannik Sinner in his 10th attempt at reaching a slam semi-final.
"I started to tell to myself, "you're going to die today but you will do everything" (in the fourth set), Rublev said.
"And somehow I started to play better and better and I found more energy and I was able to win.
"He's so fast and the way he move with his legs, the speed was crazy. He was super-tough to play, four hours and I'm just happy to be in a quarter-final.
"I was trying not to think about it (the pain), I was just trying to push myself, I was going to do everything I could - don't cry, don't feel sorry for yourself. Stop these things and keep fighting.
"Better not to be inside my head. It's like a scary movie, a lot of emotions."
Rublev claimed the first set when de Minaur double-faulted on set point.
Rublev celebrated one of the best wins of his career in the terrific five-setter. (Lukas Coch/AAP PHOTOS)
The world No.5 barely missed a beat early in the second set but de Minaur hung in to take it to a tiebreak.
Then the Australian kicked into overdrive, pulling off an audacious shot around the net when trailing 2-1 to draw level, and converting his second set point with a brilliant lob.
De Minaur raced away to a 3-0 lead in the third set as Rublev grew increasingly frustrated.
The 24-year-old got shaky when serving for the set and let the opportunity slip, and Rublev saved a second set point on serve to force a tie break.
De Minaur claimed the tiebreak, and a two-sets-to-one advantage with a wonderful passing shot.
But Rublev almost immediately seized control of the fourth set, racing away then claiming it.
He kicked into another gear in the decider, leaving de Minaur to rue what might have been.
