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.
Spanish world number two Carlos Alcaraz also exited the Paris Masters on Thursday.
The 21-year-old four-time major winner forced a deciding set against Frenchman Ugo Humbert, but lost out 6-1 3-6 7-5 to the home favourite who recorded the joint-biggest victory of his career.
