Baptiste struck seven aces and saved five of nine break points to win in two hours and six minutes. Up next is No. 5 seed Liudmila Samsonova of Russia, a 6-2, 6-2 winner against Indonesia's Janice Tjen.
No. 3 seed Clara Tauson of Denmark and American McCartney Kessler will meet in another quarter-final after their straight-set victories. Tauson took out Switzerland's Simona Waltert 6-3, 6-1, and Kessler upended No. 6 Leylah Fernandez of Canada 6-3, 6-2.
Transylvania Open
No. 2 seed and home favourite Jaqueline Cristian survived a 6-2, 2-6, 7-5 challenge from Italy's Lucrezia Stefanini in a first-round match in Cluj-Napoca, Romania.
Cristian converted four of five break points in the two-hour, 18-minute match, including a crucial break in the 11th game of the decisive set before serving out the match. Cristian's second-round opponent will be Ukraine's Daria Snigur, who defeated France's Tiantsoa Rakotomanga Rajaonah 6-3, 6-3.
In other first-round action, No. 4 seed Xinyu Wang of China defeated Spain's Kaitlin Quevedo 6-3, 6-0 and No. 5 Anastasia Potapova of Austria beat Italy's Lucia Bronzetti 5-7, 6-4, 7-5.
Ukraine's Oleksandra Oliynykova moved into the quarter-finals with a 6-4, 6-4 upset of No. 8 Anna Bondar of Hungary. China's Yue Yuan also made the quarters, outlasting Spain's Sara Sorribes Tormo 4-6, 6-2, 7-6(5) in three hours and 24 minutes.
Ostrava Open
Unseeded American Katie Volynets knocked off No. 1 seed Tatjana Maria of Germany 7-5, 6-1 to advance to the quarter-finals in the Czech Republic.
Volynets saved three of four break points and converted five of 11 break opportunities to set up a meeting with US compatriot Alycia Parks, who notched a 6-4, 6-2 victory over Armenia's Elina Avanesyan.
Sixth-seeded American Caty McNally also made the quarterfinals with a 6-4, 6-4 win over Czech Tereza Martincova. In first-round action, No. 4 seed Rebecca Sramkova of Slovakia beat Czech Vendula Valdmannova 6-2, 6-3, and No. 5 Viktorija Golubic of Switzerland defeated Austria's Sinja Kraus 6-4, 6-0. Britain's Katie Boulter was a 6-4, 3-6, 6-1 survivor against Czech Lucie Havlickova.