Pegula posted a 6-3, 6-4 victory over 24th-ranked Qinwen Zheng (20) of China in 1 hour, 38 minutes, while Gauff fired six aces en route to a 6-3, 6-2 win over Bernarda Pera (28) in 61 minutes.

Pegula and Gauff could meet in the quarterfinals, provided they win their second-round matches on Wednesday against Colombian qualifier Camila Osorio (21) and lucky loser Jodie Burrage (24) of Great Britain, respectively.

Also on Tuesday, Frenchwoman Caroline Garcia (29) secured a 6-1, 7-5 win over Madison Brengle (33) and fourth-seeded Ons Jabeur (28) of Tunisia captured a 6-3, 6-2 victory over Italian Jasmine Paolini (27).

Eighth-seeded Beatriz Haddad Maia (27) had a much tougher time of it before notching a 3-6, 6-3, 7-6 (3) win over Marie Bouzkova (24) of the Czech Republic.

Bad Homburg Open

Second-seeded Liudmila Samsonova (24) outlasted Linda Noskova (18) of the Czech Republic to punch her ticket to the quarter finals.

Samsonova recorded 18 aces to secure a 6-4, 7-6 (4), 6-3 win over Noskova.

Fifth-seeded Bianca Andreescu (23) was not as fortunate. Spain's Rebeka Masarova (23) registered seven aces en route to a comprehensive 6-3, 6-2 victory over the Canadian, a former US Open champion and the runner-up at this tournament last year.

Also on Tuesday, eighth-seeded Varvara Gracheva (22) notched a 6-2, 7-5 win over Italian Sara Errani (36).