And no one, from his fellow players to coaches and commentators, is saying he cannot continue his adventure, even though his next opponent in the last 16 on Monday is the No8 seed Andrey Rublev, a man with significantly more experience.
That includes Rublev, who will be trying to make the quarter-finals of a Slam for the ninth time in his career.
“Jack is a very talented player, he’s playing really good,” Rublev said ahead of their clash here in New York.
“We had a couple of matches which were really tough. I like his style of playing a lot. He has a huge serve, really great forehand, great backhand and can play aggressive. He has everything to become a top player.”
What makes Draper’s run to the fourth round of a Slam for the first time even more remarkable is that he had played barely any tennis over the past few months.
When the left-hander sustained a shoulder injury at the French Open in May, he thought he would be back on court in a week.
Instead, he missed Wimbledon and even the week before the US Open, when he felt some pain during the Winston-Salem event, he rated himself a 30-70 chance to even play here.
But right from the start, the 21-year-old has looked at home, revelling on his return to Flushing Meadows, where he reached the third round last year.
A first-round win over Radu Albot was followed by a stunning straight-sets win over No17 seed Hubert Hurkacz and he saw off Michael Mmoh in four sets to advance to week two.
In February this year, Draper reached a career-high ranking of 38. In his absence from the Tour, he has slipped to 123, but his run here will take him close to the top 100 and, should he beat Rublev, he will be inside the top 80 again.
After going through a series of injuries, there is a maturity to Draper that might not have been so evident had things all been easy. Nothing seems to faze him too much, which helps him on court when things get tough. And inside, there is a real steel.
“I’m not here just to be here and be happy to play,” he said. “I’m a competitor when I get into the matches. I want to win everything.
“Definitely at the start of the week, there was real concern about my body and, with the year I’ve had, whether I’d be able to, you know, play one match. Obviously, best-of-five sets, it’s completely different to what a three-set match even holds.
“To come here this week and to play the way I have and to compete the way I have, and for my body to hold up... it’s been pretty special for me, really.”
The good thing for Draper is that, as Dan Evans pointed out, he does not fear anyone.
“He’s sure of his game and he’s very good at tennis and he’s not fussed about a ranking or a name,” Evans said. “That’s a good thing and he’s impressive when he plays against the good players.”