Muguruza was valiant and tried to mount a comeback, however, having a second chance to serve for the match at 5-4, Hsieh did not think twice as she raced to victory.
The 32-year-old Taiwanese had previously managed only two wins over top 20 players in her 17 years as a professional.
Hsieh, advancing to face 26th seed Agnieszka Radwanska in the third round, was delighted with her mental fortitude against a top ranked player. "I think I deserve to smile out there after that victory". I do a little bit better today and try to hang in there. I was thinking, 'Ah, I'm from Asia. "I was going pretty good when I was hanging there".
She certainly handled the furnace-like conditions better than Muguruza, who needed treatment early on for her heat-blistered feet.
MEN, 2ND RD: Tennys Sandgren (USA) bt Stanislas Wawrinka (Sui) 6-2 6-1 6-4, Roger Federer (Sui) bt Jan-Lennard Struff (Ger) 6-4 6-4 7-6 (7-4), Marton Fucsovics (Hun) bt Sam Querrey (USA) 6-4 7-6 (8-6) 4-6 6-2, Nicolas Kicker (Arg) bt Lukas Lacko (Svk) 6-2 7-5 1-6 7-5, Novak Djokovic (Srb) bt Gael Monfils (Fra) 4-6 6-3 6-1 6-3, Julien Benneteau (Fra) bt David Goffin (Bel) 1-6 7-6 (7-5) 6-1 7-6 (7-4).
Ninth-seeded Johanna Konta, the 2016 Australian Open semifinalist, went down to United States lucky loser Bernarda Pera 6-4 7-5.
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World No.1 Simona Halep has shrugged off concerns about her injured ankle, breezing into the third round of the Australian Open with a straight-sets win over Eugenie Bouchard. "I maybe can handle it better than other girls", mentioned Hsieh during her post-match press conference.
It was an honest appraisal.
Hsieh, who plays with a two-handed slice forehand, took a 5-2 lead in the first set and, although Muguruza fought back to force a tie-break, it was the Chinese Taipei player who took it.
Hsieh was especially productive on her backhand, guiding 12 winners past her opponent, the last one coming on match point.
"I knew she was going to give me a lot of pressure", said Hsieh, who was ranked number one in doubles for five weeks in 2014. The Rod Laver Arena court surface was 69 deg C. I hit the ball very well. I try to practice all the stuff.
French eighth seed Caroline Garcia narrowly avoided elimination, battling back from a third-set deficit to see off Czech Marketa Vondrousova 6-7 (3-7) 6-2 8-6 in a two-and-half-hour scrap, played out in the searing early-afternoon heat.