Little known prior to his great run in Brisbane last week, the 18-year-old is fast pushing himself forward as Australia's hottest teenage talent.
His latest victory came against Feliciano Lopez, a player twice De Minaur's age who made his ATP Tour debut before the Sydney youngster was even born.
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But De Minaur proved too steady, winning 6-4 6-4 to become the youngest male semi-finalist at the event in nearly 30 years.
In the last four he will face France's Benoit Paire, who knocked out defending champion Gilles Muller by the same scoreline.
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Fourth seed Fabio Fognini won the closest match of the day, 6-7 (4/7) 7-6 (7/4) 6-2 against Adrian Mannarino, and will take on young Russian Daniil Medvedev, who defeated Paolo Lorenzi 6-3 6-3.
Juan Martin del Potro was already guaranteed to return to the top 10 for the first time since 2014 and he kept his run going at the ASB Classic in Auckland.
The popular Argentinian did not face a break point in a 7-6 (7/4) 6-3 victory over Russian Karen Khachanov to reach the semi-finals.
Del Potro will take on veteran David Ferrer in the last four, with the Spaniard easing to a 6-3 6-2 win over young Korean Chung Hyeon.
The other semi-final will pit fifth seed Roberto Bautista Agut, a 7-6 (7/1) 6-2 winner over Jiri Vesely, against Robin Haase, who defeated Peter Gojowczyk 6-4 6-4.
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