Spanish tennis player Paula Badosa. AFP
After comfortably pocketing the first set with two breaks of serve, Spain's Badosa went down an early break in the second against her 240th-ranked opponent, who is the daughter of four-time Grand Slam champion Hana Mandlikova.
She broke back, but was broken again in the 11th game to give Mandlik a chance to serve out the set and extend the match.
After breaking for a 4-3 lead in the third, Mandlik twice had a chance to serve for the set, but they traded service breaks in the final three games to send it to the tiebreaker, in which world number four Badosa won the last five points to seal the victory.
Badosa will next face the winner of Thursday night's marquee clash between four-time Grand Slam champion Naomi Osaka and sixth-seeded American Coco Gauff.
Japanese superstar Osaka is unseeded as she plays her first tournament since falling in the first round of the French Open, where she was battling a left Achilles tendon injury.
Gauff, the French Open runner-up, is seeded sixth.
Third-seeded Tunisian star Ons Jabeur, playing her first match since her historic runner-up finish at Wimbledon, pulled away late to beat American Madison Keys 7-5, 6-1.
Jabeur will face either Veronika Kudermetova or Claire Liu in Friday's quarter-finals.
Jabeur got off to a strong start with an early break for a 2-0 lead before Keys surged to a 5-3 lead.
Jabeur responded by winning 10 of the next 11 games.
"I'm grateful that I played at night because it's slower and it helps me a little bit with the conditions," Jabeur said. "I knew it was going to be a tough match for me. I just tried to stay low and hit the ball as much as I can. Make her play another ball and in the end I was feeling much better."
American Amanda Anisimova beat Czech Karolina Pliskova for the first time in five attempts to reach the quarter-finals.
Anisimova trailed by a set and a break on the way to a 3-6, 7-5, 6-1 victory.
Seventh-seeded Daria Kasatkina also advanced, beating American Taylor Townsend 6-4, 6-0.
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