Anisimova, Cornet and Badosa recover to advance in Charleston
Number 13 seed Anisimova came from a set down to beat Magda Linette 5-7 6-2 6-3 on Monday, dropping serve only once in those last two sets.
Cornet, who reached the quarter-finals of this event in 2018, needed just under three hours to overcome Bernarda Pera 4-6 6-4 6-4.
Badosa also needed all three sets to see off Varvara Gracheva, the Spaniard hitting back to prevail 3-6 7-5 6-1.
Ajla Tomljanovic and Zarina Diyas were also among those to book a place in the next round, beating Christina McHale and Natalia Vikhlyantseva respectively in straight sets.
In the other WTA Tour event, Copa Colsanitas top seed Zheng Saisai eased past Usue Maitane Arconada 6-3 6-1 and will now face Stefanie Voegele.
Wang Yafan was another Chinese player to advance in Bogota, seeing off Emiliana Arango 6-4 5-7 7-5.
Get breaking news alerts.
You have already subscribed