Errani came out strong, winning the first seven games of the match to lead 6-0, 1-0, but Domínguez Lino came alive from there, matching Errani shot for shot from the baseline to stay very even for the next hour - 1-all, 2-all, 3-all and so on until the two players were locked at 5-all in the second set.
That's when the No.1-seeded Errani pounced, breaking one last time and then fighting off three break points in the next game to close out the 65-minute second set and finally the match, 6-0, 7-5.
"I'm in the quarterfinals now, so I still just want to think match by match, but of course I hope I can win the title here," Errani said after the match. "There are a lot of difficult players here in Rio de Janeiro. It's not easy to think ahead like that - I just have to think about my next opponent and that's all."
The 18-year-old Haddad Maia's win is something of a milestone - she's just the second Brazilian since 1999 to reach a WTA quarterfinal, after Teliana Pereira (who has done it twice since then).
"It was the best match of my life," Schmiedlova recalled. "I played really well that day. I couldn't believe I beat such a good player on center court. She played really well that day too, but I was moving well, and I was so happy I managed to win it. To me it's still the best match I've ever played.
"I really like playing on clay. And of course I like playing on the clay here in Rio."
Both Schmiedlova and Cepede Royg will be playing the first WTA quarterfinals of their careers.
Errani against Haddad Maia and Schmiedlova against Cepede Royg will both be first-time meetings.