A quarter-finalist in Melbourne past year, the second-round defeat was Muguruza's earliest at the season's opening grand slam since she was beaten at the same stage in 2013.
But the Spaniard, 24, had no remedy when her heaviest hits were returned in unusual places.
The five-time major victor advanced to the third round with a 6-1, 7-6 (4) win over No. 14-seeded Anastasija Sevastova.
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.
The Australian Open, which kicked off Monday, will run through January 28 in Melbourne.
WOMEN, 2ND RD Bernarda Pera (USA) bt Johanna Konta (Gbr) 6-4 7-5, Karolina Pliskova (Cze) bt Beatriz Haddad Maia (Bra) 6-1 6-1, Naomi Osaka (Jpn) bt Elena Vesnina (Rus) 7-6 (7-4) 6-2, Madison Keys (USA) bt Ekaterina Alexandrova (Rus) 6-0 6-1.
"I maybe could have done things better, but at the end, she deserves to win".
She will play in the third round against Angelique Kerber, the 2016 champion, who beat Donna Vekic 6-4, 6-1.
The deficit was reduced, but when the pressure mounted and Hsieh served for the match, the former doubles world No.1 managed to strike a laser-like backhand passing shot, before closing out a career-best win in style with a smartly deflected backhand victor.
"She's definitely a very tricky opponent - today she played well, " said Muguruza, acknowledging that the heat was bothersome but it wasn't the hottest conditions she'd experienced in Australia.
"Not try to play the same game".
The match was originally scheduled for Rod Laver Arena, but was moved to Margaret Court Arena due to a backlog of long matches at the larger venue.
I train this winter in Miami. I practise topspin, flat balls, slice. "I had a very tight tape".
GAEL MONFILS, the world No. 39, after being told it will be 42 deg C in Melbourne Park today. Chung advanced when Mischa retired with a viral illness while trailing 6-2, 4-1. "I did my job in two sets against someone that's been troubling in the past for me", said Sharapova, who missed last year's tournament while serving a 15-month doping ban.
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. "I want to go further than fourth round and I'll give everything to do it for the first time", he said.
"It's another tough match here", said the German world No. 16.
An exchange of breaks followed but it was a high-quality contest with both players displaying some impressive tennis, most particularly Radwanska's variety of shots going up against the crafty playing style of the underdog. "I know that I have to play my best tennis again".