But his exploits over the past week appeared to take their toll against De Minaur – who Draper beat on the way to the US Open semi-finals.
On that occasion in New York, De Minaur was physically hampered and way below his best.
This time, the 25-year-old Australian was more like his energetic self.
That spelt trouble for Draper, who looked increasingly fatigued as the contest wore on.
A tight first set swung Draper’s way when he broke serve for a second time in the 12th game before De Minaur sharpened up his groundstrokes.
Fewer loose returns from the world number 10 extended the rallies and drew energy from Draper, who was broken twice in a one-sided second set.
Draper’s frustration was demonstrated when he obliterated his racquet after going a break down in the first game of the decider.
While the Briton showed his character to level at 2-2, De Minaur continued to play at a high level and won four of the final five games to keep alive his own hopes of reaching the ATP Finals in Turin.
Stunned: Carlos Alcaraz plays a forehand return to France's Ugo Humbert (JULIEN DE ROSA)World number two Carlos Alcaraz admitted he "was not up to the level" of
Text size ADDS Alcaraz quotes World number two Carlos Alcaraz admitted he "was not up to the level" of 18th-ranked U
World number two Carlos Alcaraz (21) was knocked out of the Paris Masters by 18th-ranked Ugo Humbert (26) of France who swept to a third-round victory in three
Alex de Minaur is on the cusp of becoming the first Australian since Lleyton Hewitt in 2004 to qualify for the ATP Finals after exacting revenge over his US Ope