Pallikal, the highest-ranked player in the qualifying draw, beat Whitlock 11-6 11-8 11-6 in the first qualifying round of the WSA Gold event at the Princeton Club.
The Chennai girl will now face Hong Kong's Annie Au for a place in the main draw for the third year in a row.
In the men's event, India's No.1 player Saurav Ghosal will open his campaign against Germany's Simon Rosner.
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