At the Charleston Open, 2011 champion Wozniacki battled past Mihaela Buzarnescu 6-4 3-6 6-3 in the third round.
Wozniacki will meet Maria Sakkari in the quarters after the Greek 15th seed beat defending champion Kiki Bertens 7-6 (10-8) 6-3.
In the top half of the draw, Sloane Stephens and Madison Keys will face off in a blockbuster all-American quarterfinal.
Stephens, the 2016 champion, edged Ajla Tomljanovic 4-6 6-4 6-4, while Keys was too strong for Jelena Ostapenko 7-5 6-2 in a clash between two former runners-up.
Petra Martic and Belinda Bencic will meet, while Danielle Collins faces Monica Puig.
Puig is the only unseeded player remaining in the draw after the Puerto Rican upset Aryna Sabalenka 6-2 7-5.
Meanwhile Angelique Kerber and Garbine Muguruza continued their runs at the Monterrey Open, while Caroline Wozniacki advanced in Charleston on Thursday.
Kerber, the top seed at the WTA International event in Mexico, was too good for Karolina Muchova 6-3 6-4 in the second round.
The German two-time runner-up powered into the quarter-finals, where Kirsten Flipkens awaits.
Muguruza's title defence remains alive after the Spanish second seed overcame Margarita Gasparyan 6-3 6-7 (1-7) 6-2.
Awaiting her in the last eight is Kristina Mladenovic, who eased past 39-year-old lucky loser Greta Arn 6-0 6-2.
Also progressing in Monterrey on Thursday was two-time grand slam champion Victoria Azarenka, the Belarusian beating Zarina Diyas 6-3 6-2.