Collins, an American who was the runner-up at the 2022 Australian Open, saved both break points she faced while claiming five of McNally’s service games.
Collins is the highest-seeded player remaining in the field at the inaugural edition of the hard-court tournament in the Texas capital.
She’ll try to reach her first semifinal of the year by next beating 67th-ranked Anna Kalinskaya of Russia, who was a 6-3, 6-1 winner against CoCo Vandeweghe on Thursday.
Kostyuk breezed through the final set to beat Madison Brengle 6-3, 3-6, 6-0 and reach her third quarterfinal of 2023. Kostyuk, a 20-year-old from Ukraine, made it only as far as the quarterfinals at one event all of last season.
The 108th-ranked Friedsam edged Erika Andreeva 7-5, 6-7 (2), 7-6 (8). For the 29-year-old Friedsam, it marks the first time the German player has won back-to-back tour-level matches in North America in her career.