The 26-year-old New South Welshman trounced seventh seed Alex Michelsen 6-0 4-6 6-1 on Thursday (Friday AEDT) to book his spot in the last eight of the ATP Tour's claycourt event, where he'll face another American in Frances Tiafoe.
Second seed Tiafoe began his campaign with a 6-4 3-6 6-2 victory against another Aussie in Rinky Hijikata.
Popyrin broke three times in the opening set to take it in just 23 minutes, but the 35th-ranked Michelsen took it to a decider where he was again blown off the court.
Up next for Popyrin is Tiafoe, who was playing his first event on clay since reaching the Roland Garros quarter-finals in 2025.
With NBA star Kevin Durant among those in the crowd, 2023 champion Tiafoe displayed his trademark shotmaking ability throughout the two-hour 28-minute clash, as did Hijikata.
After reaching the fourth round at Indian Wells, 25-year-old Sydneysider failed to qualify for the Miami main draw but beat Aleksandar Kovacevic in straight sets to set up the Tiafoe clash.
The 28-year-old former world No.10 proved too tough a nut to crack though and is 14-0 after winning the first set this season.
"First match on clay was definitely funny. I was still doing some stuff I was doing on a hard court just trying to get my feet under me," said world No.18 Tiafoe, who's into the Houston quarters for the fifth consecutive year.
"But it's good. I got to play a couple hours out here. I'm happy to get through and get another chance to play a bit better tomorrow."
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