Isner fired 29 aces but needed two hours and 24 minutes to get past the tenacious 19-year-old, whose elder brother Ryan Harrison booked a quarter-final berth earlier in the day.
Christian Harrison had made his ATP Tour singles debut on Wednesday with a victory over Alejandro Falla -- surprising many but not his older brother.
"I think a lot of people were shocked, but I wasn't shocked, he wasn't shocked, he has that expectation of himself where he feels he belongs," said Ryan Harrison, who reached the last eight with a 6-4, 6-3 victory over fourth-seeded Igor Sijsling of the Netherlands.
Harrison will play Colombian Santiago Giraldo who was leading Michael Russell 5-7, 6-3, 3-0 when the American retired from their match.
Isner will play compatriot James Blake, who reached his first quarter-final of the season with a brisk 6-3, 6-2 victory over eighth-seeded Russian Evgeny Donskoy 6-3, 6-2.
Blake broke Donskoy's serve three times and saved all four break points he faced in the 64-minute encounter.
"I always feel like the hard-court summer is my best chance to get points, I'm playing my best tennis," Blake said. "The courts usually suit me the best. When it's hot I play pretty well. Home crowds in the States, it's generally my favourite time of the year. This is a good start to it right away."
In other second-round matches, Uzbekistan's Denis Istomin defeated fifth seed Lu Yen-Hsun of Taiwan 7-5, 6-2.
Istomin will play second-seeded South African Kevin Anderson, who beat Australian qualifier Matthew Ebden 6-7 (7/9), 6-2, 6-2.
The remaining quarter-final was set on Wednesday, when seventh-seeded Australian Lleyton Hewitt advanced to a meeting with Croatian Ivan Dodig.