De Minaur came into the clash on Rod Laver Arena having won three of his four matches with the hard-hitting Tiafoe, but the 26-year-old had to weather a storm on serve in the seventh game before breaking in the next and surging ahead.
With the opening set in the bag, De Minaur showcased his sublime court coverage to break again for a 2-1 lead in the next set and stayed on top despite a minor wobble to leave Tiafoe staring at another defeat in their rivalry.
A spectacular backhand winner from deep handed De Minaur another break at the start of the third set, and though Tiafoe clawed his way back and then went up 5-4, the home favourite composed himself to edge ahead again and prevail.
"Frances is a hell of a competitor, a hell of a player and it was a hell of a battle," he said.
"Huge respect to him. I played some of my best tennis in the tournament for two and a half sets, and he lifted his game when he needed it, started going big and got some big winners.
"I had to manage it. It was stressful in the end, but I'm relieved I got over the line."
The sixth seed's efficient victory ensured he became only the second Australian man in the professional era to go on such a streak after John Newcombe, who reached the last 16 at the tournament from 1969-76.
Half a century has passed since Mark Edmondson lifted the trophy at the Australian Open and the country's drought on the men's side inevitably frames expectations around De Minaur, but he is not heaping pressure on himself.
"In my brain... I don't associate playing in Australia as playing with pressure. I associate it with just excitement," De Minaur said about managing Australian expectations at his home Grand Slam, where he has not gone past the quarter-finals.
"Since I was a little kid, this is where I wanted to be and where I wanted to play, in front of packed crowds. I'm truly fortunate to be in this position and yes, it gets stressful at times, but that's only because I want it so bad. So I'll do my best."
