Draper’s run is beginning to bring back memories of fellow Briton Emma Raducanu’s stunning victory at the US Open three years ago.
Like Raducanu, Draper has reached the last four without losing a set, moving through the draw with ease.
But while Raducanu’s remarkable win came from nowhere, Draper’s showing comes after a year where he has steadily delivered on his long-heralded talent.
Draper was a Wimbledon runner-up as a junior and took a set off Novak Djokovic on Centre Court when he made his Grand Slam debut aged 19.
Injuries last year meant that, despite reaching the fourth round in New York, he was outside the world’s top 100 just 12 months ago.
But this year he has risen steadily, becoming British number one in June and now making his name on the biggest stage.
After a serene run to the last eight, he had to deal with the distractions of both his own physical issues and those of his opponent, who was struggling badly by the end.
After the winning point Draper remained remarkably calm, carefully rearranging his belongings rather than being overcome with emotion – a suggestion he feels there is more to come.
He will go into the match against Sinner or Medvedev as a huge underdog, but history suggests special things can happen to Britons in New York.