De Minaur came up against Japanese qualifier Rei Sakamoto - a 20-year-old ranked 137th compared to the Australia's No.9 seed and world ranking.
The 27-year-old de Minaur had to dig deep but ultimately prevailed 7-6 (8-6) 6-4 in an hour and 34 minutes to progress to a meeting with 26th-seeded Russian Karen Khachanov.
De Minaur and Sakamoto held serve comfortably through the first set, with three holds to 30 by Sakamoto being as close as either player came to conceding a break.
The Australian snatched a mini-break in the tiebreaker to lead 4-2, and after holding his next two service points led 6-3. Sakamoto hit back with a mini-break to make it 6-6, but de Minaur held then broke his rival immediately and closed out the set.
Both players held serve comfortably again in the second set before de Minaur grabbed a break from deuce to lead 3-2. He then staved off the only two break points against him for the match to hold for 4-2, which proved the decisive margin.
In a match of inches, De Minaur converted his only break point opportunity, while Sakamoto converted none from two.
De Minaur won 92 per cent of his first serve points compared with Sakamoto's 71 per cent, and shaded second serve points by 62 to 58 per cent.
Earlier, US Open finalist Ben Shelton conceded he had been "outplayed" after a shock 7-6 (7-5) 7-6 (7-3) defeat from France's Arthur Gea in the third round.
World number four Shelton, who has barely played since losing to Alexander Zverev in September's US Open final and withdrew from the recent Japan Open due to fitness concerns, lost both sets against the world number 56 in tight tiebreakers.
Asked if his recent lack of action had had an effect on him, Shelton told reporters: "I mean, I got outplayed today. The guy played better than me.
"A hundred per cent, I would have liked to have come over here earlier and be prepared and have already dealt with the jet lag by the time I was playing here in the Shanghai Masters.
"My body wasn't ready. I wasn't physically ready to play in Tokyo. That's just the way this tour is sometimes."
The 24-year-old American said he was focused on finishing his 2026 campaign on a "high note" at the season-ending ATP Finals in Turin next month.
Gea, who next faces 13th seed Jakub Mensik, was delighted with his first win over a top-10 player.
"I'm practising hard every day since the beginning of the year to win against those guys," he said.
- With Reuters.
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