The third seed, whose preparation was hampered by a thigh injury, was always trailing against the world number 88 before being edged out 7-6 (7/1), 6-4 in one hour and 59 minutes on Rod Laver Arena.
"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.
Two-time Grand Slam champion Muguruza struggled from the start to keep pace with the tenacious 32-year-old whose last WTA Tour singles title came at Guangzhou back in 2012.
The tall Spaniard had a medical timeout at 2-5 in the first set and after having a foot re-taped looked briefly regalvanized.
Muguruza broke back twice but Hsieh, who works closely with former Australian Open tournament director Paul McNamee, ran away with the tiebreak 7-1.
"He's always been around me and supported me and was amazing," she said of McNamee's influence.
"My goal to hire him at the beginning was to win a Grand Slam," she added.
Muguruza saved a first match point in the second set to get back to 5-4 but Hsieh made no mistake in the next game.
"At 5-4 I thought I'd keep hanging there and try and take my spot," she said.
Hsieh, whose previous best at Melbourne Park was a last-16 defeat to Justine Henin 10 years ago, goes on to meet 26th seed Agnieszka Radwanska of Poland in the third round.