But Hewitt found his feet, breaking back in the sixth game and holding serve before succumbing 6-2.
Cheered on by a crowd that included his famous father, Hewitt started the second set brightly.
But he was broken again on his second service game and could not reel in De Minaur, who warmly embraced the youngster at the net after taking the match.
It was the first head-to-head ATP Tour match between the two, who have known each other for years.
“It was definitely weird,” De Minaur said. “I knew I was going to play him on the tour someday, but I didn’t actually expect it to be this week.
“It was an amazing feeling. Even all the lead-up, seeing all the incredible pictures that we have together and how we’ve both grown up.”
“I’m glad I managed to get through, but I’m sure we’re going to have many battles in the years to come.”
De Minaur next faces American Brandon Nakashima, who upset Czech seventh seed Jakub Mensik 7-6 (7/5), 3-6, 6-4.
US home hope Shelton advanced with a gritty victory over France’s Humbert. After handing Humbert the first set with a double fault on set point, Shelton dominated the second.
But the third set was a tense affair and after seizing a break for a 5-4 lead, Shelton had to fend off a break point before polishing off the match with a sharply angled serve that Humbert smacked into the net.
“For me, it was all about heart tonight,” Shelton said after lining up a meeting with Chile’s Alejandro Tabile, a 6-3, 7-6 (8/6) winner over France’s Terence Atmane.
Pegula also had to rally from a set down, saying she started her match against Poland’s Frech “just a little off” after a first-round bye.
“I wasn’t quite attacking the ball, and I felt like once I did that, then everything else kind of started to click together,” said Pegula, who finished with 42 winners and won 12 of the last 15 games.
Pegula next plays fifth-seeded Anna Kalinskaya, who saved two match points to beat Indonesia’s Janice Tjen 1-6, 6-3, 7-6 (9/7).