This is unfamiliar territory for Draper, his previous best performance having been a fourth round appearance in New York last year.
This will be the first time the British players will play at the 23,771-capacity Arthur Ashe Stadium – a venue they visit every day while in the city.
But it has been a successful year for Draper, winning his first ATP Tour title in June with an eye-catching win over Wimbledon champion Alcaraz at Queens.
He is now at a career-best 25th in the world rankings.
“He’s managed to stay on the tour for a longer period of time so he’s got more experience,” Great Britain Davis Cup captain Leon Smith told BBC Sport.
“He is getting more experience. He participates in big competitions more often. This is helping him understand how to handle himself better.”
His quarterfinal opponent de Minaur is undoubtedly the more experienced one. He has nine ATP titles to his name and has reached the last eight at three consecutive Slams.
He also leads in head-to-head competition, having won all three of his matches against Draper.
But, like Draper, the 25-year-old Australian has never reached a major semi-final.
“You’re expecting de Minaur to make it awkward and difficult,” Bartoli said.
“Jack’s got to hit it across the court and keep attacking it.”