The world No.6 endured some nervous moments to progress to the round-of-16, winning 6-3 6-4 7-5 against big-hitting American Frances Tiafoe on Friday night.
He will next meet 10th seed Alexander Bublik, who beat Tomas Martin Etcheverry 7-6 (7-4) 7-6 (7-5) 6-4, before a potential quarter-final with world No.1 Carlos Alcaraz.
It took de Minaur two hours 43 minutes to take down the 29th seed Tiafoe, who never gave up on Rod Laver Arena.
In his first match of the tournament against a seeded opponent, de Minaur completed his fourth win from five outings against the talented, but often-wayward Tiafoe.
The dual major semi-finalist virtually handed the first set to de Minaur due to a series of unforced errors.
De Minaur broke serve twice during the second set and appeared to be crushing Tiafoe's spirit.
But Tiafoe did pull one of the breaks back to force de Minaur to close out the set.
A short break at the start of the third set due to a person in the crowd falling unwell didn't seem to immediately halt the rampant Australian's momentum.
Tiafoe gave de Minaur a slight scare towards the end, getting back on serve and defending match points.
But 'Demon' broke back at 5-5, before serving for the match.
"Frances is a hell of a competitor, a hell of a player, it was a hell of a battle," de Minaur said.
"I played some of my best tennis in the tournament for two and a half sets, and he just lifted it when he needed it.
"In my brain, I don't associate playing in Australia with pressure, I associate it with just excitement.
"I've known since I was a little kid this is where I wanted to be, where I wanted to play, in front of packed crowds.
"I'm truly fortunate to be in this position.
"Yes, it gets stressful at times, but that's only because I want it so bad, so I'll do my best."
Despite having never progressed past the quarter-finals at Melbourne Park, de Minaur is in rare air.
Not since the legendary Newcombe from 1969 to 1976 has an Australian man reached the fourth round of their home grand slam in five-straight years.
De Minaur is also the first Australian man to make five fourth-round appearances at Melbourne Park since Lleyton Hewitt, who achieved the feat seven times between 2000 and 2012.
He equals Pat Cash and Mark Philippoussis in sixth place for most round-of-16 appearances at a grand slam by an Australian man.
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