Sixth-seeded Pegula beat her fellow American 6-4, 4-6, 7-6 (6) on her seventh match point to reach the third round.
Pegula, who lost in the China Open semifinals last week, will next play ninth-seeded Ekaterina Alexandrova, who beat American Ann Li 7-6 (5), 6-2.
No. 3 Coco Gauff, coming off a semifinal loss to eventual champion Amanda Anisimova at the China Open last week, breezed into the next round with a 6-1, 6-0 win over Moyuka Uchijima in 51 minutes.
Also, qualifier Kateřina Siniaková beat Maya Joint 6-3, 6-1.
Eleventh-seeded Naomi Osaka was upset by unseeded Linda Noskova 7-6 (2), 6-3. The 20-year-old inform Czech was defeated by Amanda Anisimova in the final of the China Open on Sunday.
Noskova, ranked 17th, will next face either Jaqueline Cristian or Elena Rybakina.
