Muguruza started perfectly with a break of serve, but Su-Wei hit back with two of her own to take a 4-1 lead in the opening set.
The Spaniard responded by winning four of the next five games, but crumbled in the tie-break as Hsieh took it 7-1.
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Highlights: Muguruza outfoxed by Hsieh in Melbourne sunshine
Muguruza, who withdrew from the Sydney International last week, was succumbing to both the Melbourne heat and her fearless opponent in the second set.
Hsieh broke serve twice to race ahead, and though she failed to serve for the set at the first time of asking, Chinese Taipei's Su-Wei, 32, made no mistake the second time around.
Su-Wei’s reward for producing the biggest shock of the tournament so far is a third round match against 26th seed Agnieszka Radwanska.
Meanwhile, Muguruza joins other seeds Venus Williams, Sloane Stephens, Coco Vandeweghe, Kristina Mladenovic and Johanna Konta as early departures from the women's draw.
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