Hsu, ranked 505th in the world, ousted the 242nd ranked Ankita 7-6 (6) 6-2 in two hours and seven minutes to enter the second round in singles here.
In the opening set, which went to the tie-break, Ankita missed a forehand at 5-5 and let the qualifier surge ahead to capture it.
In the second, the Indian girl looked jaded, was down 1-4 and could not make a comeback, losing the set tamely and with that the match.
Also making their exit from the singles were other Indian players Sri Vaishnavi Peddi Reddy, a qualifier, lucky loser Snehadevi Reddy and wild card Prarthana Thombare.
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Katy Dunne Britain outplayed Sri Vaishnavi 6-4 6-3, while winner of the title here last year -- Dalila Jakupovic -- of Slovakia scored an identical win over Snehadevi to make it to round two.
Top seed Magda Linette proved too strong for India No. 2 Prarthana G Thombare, winning 6-3 7-5 in less than two hours.
Dart, ranked 430, broke her Thai rival in the 11th game of the first set and the 3rd game of the second set to earn the victory in two hours and 25 minutes.
Other results:
Singles (1st round): Riko Sawayanagi (JPN) (6) bt Cristina Ene (ROU) 2-6 6-0 6-2; Xinyun Han (CHN) (8) bt Britt Geukens (BEL) 6-2 6-2.
Doubles (1st round): Ya-Hsuan Lee/V Wongteanchai (Thai,3) b Natasha Palha/ Rishika Sunkara (Ind) 6-3 6-2; Kai-Lin Zhang/ Yukun Zhang (Chn) b Bhuvana Kalva/ Rashmi Teltumbde (Ind) 6-3 6-0l; Nidhi Chilumula/ Prarthana Thombare b Snehadevi S Reddy/ Dhruthi Venugopal 5-7 6-3 10-6.