Draper earlier this month became the first British man to make the US Open last four since Andy Murray won the title 12 years ago, but found his path to the final blocked by eventual champion Jannik Sinner.
Draper has picked up where he left off in Tokyo, beating Hurkacz in one hour and 24 minutes to set up a quarter-final against either American Brandon Nakashima or France's Ugo Humbert.
Hurkacz's exit means only three of the eight seeded players remain at the Japan Open.
Number one Taylor Fritz, number three Casper Ruud, number four Stefanos Tsitsipas and number seven Frances Tiafoe all lost in the first round.
Draper, who is ranked 20th in the world, is unseeded in Tokyo.
He has come back from multiple shoulder injuries and was ranked outside the top 100 when he played at the Japan Open last year.
