World number 51 Anand took just 29 minutes to get the better of Hsueh 21-15 21-13 in the round of 16.
Anand will now face the winners of the match between second seed Boonsak Ponsana of Thailand and 16th seed Niluka Karunaratne of Sri Lanka.
Anand's compatriot Ajay Jayaram will face eighth seed Tommy Sugiarto of Indonesia in the pre-quarters later.
However, it was curtains for senior shuttler Arvind Bhat, who suffered a 10-21 16-21 loss to Ponsana in another men's singles match which lasted for just over half an hour.
In men's doubles, Tarun Kona and Arun Vishnu crashed out after losing 16-21 17-21 to V Shem Goh and Khim Wah Lim in the opening round.
Anand Pawar reaches quarter-final of German Open badminton
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