There would be no escape this time as Hsieh guided away a backhand victor on her second match point to claim the biggest singles victory of her 17-year career.
Hsieh, who is 88th in the world rankings, warmed up quickly, losing only two games to Radwanska to finish 6-2 in the first set.
Muguruza had played just one full match to begin the year after retiring at the Brisbane International due to cramps and withdrawing in Sydney because of a thigh injury. Find us on Facebook too!
Pilskova set up an all-Czech third-round affair with Lucie Safarova, a 6-2 6-4 victor over Romania's Sorana Cirstea, while Sharapova will play fellow former world No.1 and 2016 Open champion Angelique Kerber or Croat Donna Vekic.
Sixth-seeded Pliskova romped into the third round with a 6-1 6-1 dismissal of Brazilian Beatriz Haddad Maia, joining former champion Maria Sharapova, who earlier on Thursday ousted Latvian 14th seed Anastasija Sevastosa 6-1 7-6 (7-4).
"I know the weather is going to be a little bit tough today because I hear weather going to be over 39 degrees".
Muguruza the current Wimbledon champion was put away by Su-Wei Hsieh from Taipei in what was a battle, but only for Muguruza to try and stay in the match.More news: Russian Federation offers platform for direct Afghan-Taliban talks
More news: England's Jason Roy glad to be back on track after 'tough' 2017
More news: National Football League releases schedule for 2018 games in London
Taiwanese tennis star Hsieh Su-wei (謝淑薇) rolled past Agnieszka Radwanska of Poland 6-2, 7-5 in the third round of the women's singles at the Australian Open Saturday, in a game that lasted almost 100 minutes.
No. 3-ranked Muguruza follows Venus Williams and U.S. Open champion Sloane Stephens out of the tournament in the first week, leaving only three major winners still in the women's draw - and two of them could meet in the third round.
Ninth-seeded Johanna Konta was more exposed to the heat on an outside court, and lost to USA lucky loser Bernarda Pera 6-4, 7-5. The 23-year-old Pera is making her Grand Slam debut. "I think today she played well".
Naomi Osaka clinched her match with an ace, beating local hope Ashleigh Barty 6-4, 6-2 to advance to the fourth round at Melbourne Park. I practice topspin, flat balls, slice.
"I'm nearly dead, but it was nice that we could show good tennis", Halep said. "This is the matches I'm looking forward to having, especially at the beginning of the year". "I'm happy I didn't buy one".
The big match Saturday had the only two women's major champions left in the tournament playing each other - 2008 Australian victor Maria Sharapova vs. 2016 Melbourne Park champion Angelique Kerber.
No. 5 Dominic Thiem rallied from two sets down to defeat 190th-ranked American qualifier Denis Kudla 6-7 (6), 3-6, 6-3, 6-2, 6-3.
Muguruza acknowledged that the heat was bothersome, but it wasn't the hottest conditions she'd experienced in Australia.