Rogers will face fellow American Amanda Anisimova in Friday's quarterfinals.
Fourth-seeded Aryna Sabalenka of Belarus posted a 5–7, 6–1, 7–5 win over Caroline Dolehide, and No. 9 Veronika Kudermetova of Russia beat Claire Liu 6–2, 7–5.
Citi OpenSecond-seeded Emma Raducanu of Great Britain saved nine of 13 break points while outlasting Colombia's Camila Osorio 7–6 (5), 7–6 (4) in the second round at Washington.
Raducanu and Osorio battled for two hours, 50 minutes in the longest WTA straight-sets match of 2022.
Raducanu will face Liudmila Samsonova in the quarterfinals after the Russian defeated Australia's Ajla Tomljanovic 4–6, 6–3, 6–2.
China's Xiyu Wang rallied for a 4–6, 7–5, 6–1 win over Croatia's Donna Vekic.
The scheduled match between fourth-seeded Victoria Azarenka of Belarus and Tereza Martincova of the Czech Republic was postponed due to lightning in the area.