The five-time major winner will next face Zarina Diyas, who upset third-seeded Zhang Shuai 6-3, 6-7 (5), 6-4.
"Although I would've wanted a quick and easy victory, these are the kind of matches that you need, especially with such a short preparation going into the Australian Open," Sharapova said.
Ostapenko, who beat Serena Williams in an exhibition match in Abu Dhabi on Saturday, was overwhelmed by Pliskova's powerful serves.
"I felt a bit nervous in the second set, but my serve was really working today, which was a big help," Pliskova said.
Pliskova will next play Ana Bogdan, who beat Camila Giorgi 6-4, 6-2.
Aryna Sabalenka also advanced to the quarterfinals with a 6-1, 6-0 victory over Danka Kovinic, while Timea Babos defeated Magda Linette 6-2, 6-1.