Kumar outlayed Parker 11-6 11-8 11-8 in 40 minutes.
The 18-year-old is the lone Indian remaining in the competition.
Last year, Kumar had won gold in the Asian Youth Games.
In January, he reached the quarterfinals of the U-19 British Open before finising runners-up at the Asian Championship in June.
He is ranked 220 in the senior world rankings.
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