Top seed Daria Gavrilova advanced to the San Antonio Open second round as Yanina Wickmayer was beaten on Tuesday.
Gavrilova, a wildcard for the WTA 125K Series event, survived a tough first set before beating Olga Govortsova 7-6 (10-8) 6-1 in one hour, 52 minutes.
The Russia-born Australian, who reached the last 16 at Melbourne Park, has struggled since but managed to progress after her early difficulties.
The fourth-seeded Yanina Wickmayer was unable to do the same, going down to Lauren Davis 2-6 6-1 6-3.
Another seed to fall was Teliana Pereira, the Brazilian no match for Kiki Bertens in a 6-3 6-3 defeat.
Japanese sixth seed Misaki Doi took 70 minutes to overcome Evgeniya Rodina 6-3 6-3, while Carina Witthoeft served 11 double faults but got past Jana Cepelova 3-6 6-4 6-2.
Donna Vekic edged past Aliaksandra Sasnovich 6-4 6-4, Anna-Lena Friedsam crushed Naomi Broady 6-2 6-3, Magda Linette was a 6-4 6-4 winner against Anna Tatishvili and Maria Sakkari battled past Tamira Paszek 7-6 (7-5) 3-6 6-1.