De Minaur’s training session earlier in the day lasted just 15 minutes, with doubts about his fitness even before the game began.
The 25-year-old Australian, making his fourth Grand Slam quarter-final appearance, took the first set with ease and broke serve early in the second, but was sluggish.
As Draper gained the advantage, De Minaur was clutching his hip as he threatened to reoccur the injury that forced him to withdraw from the Wimbledon quarter-finals against Djokovic.
Physiotherapists were on the pitch at the ensuing change of play, but it was to treat Draper rather than De Minaur, who had his upper thigh taped with tape.
Draper didn’t seem to be bothered too much and quickly took five break points to lead 5-2, but every break point was saved by his opponent.
This begins a run of three games in which the momentum threatens to turn in favor of the resurgent De Minaur.
Draper was struggling physically at that stage, but his powerful, swinging left-hand serve came back at crucial moments to halt his opponent’s momentum.
That horrific blow helped him end the match, and a huge forehand – his other main weapon – earned him another break early in the third game.
De Minaur launched a final challenge after one game, but the Australian’s form declined severely after winning two more break points at 3-2 on Draper’s serve.
The final set was over in just 32 minutes, with Draper becoming the third British player after Murray to reach a Grand Slam semi-final.
He will have 48 hours to recover and treat any injuries before attempting to finish Kyle Edmund at the 2018 Australian Open and Cameron Norrie at Wimbledon in 2022 The unachievable thing – advancing from the semi-finals to the finals.