In searing heat on Rod Laver Arena, the powerful Wimbledon champion never got to grips with 88th-ranked Hsieh's unusual game style and looked totally perplexed by the end.
Muguruza had battled back from 5-2 down in the opening set but 32-year-old Hsieh, who plays double-handed on both sides, pulled out all the stops to take the tiebreak 7-1.
Hsieh pulled clear in the second set with her relentless accuracy but faltered with the winning line in sight, dropping serve at 5-2.
Muguruza double-faulted at deuce in the next game to give Hsieh a match point but survived and held serve to ask the question of Hsieh's nerve for a second time.
There would be no escape this time as Hsieh guided away a backhand winner on her second match point to claim the biggest singles victory of her 17-year career.
Muguruza joins other seeds Venus Williams, Sloane Stephens, Coco Vandeweghe, Kristina Mladenovic and Johanna Konta as early departures from the women's draw.
Hsieh will face Poland's 26th seed Agnieszka Radwanska for a place in the fourth round of a grand slam singles for only the second time, having reached that stage 10 years ago here.
(Reporting by Martyn Herman; Editing by Peter Rutherford)
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