Liudmila Samsonova progressed after a marathon battle at the Dubai Tennis Championships, while Petra Kvitova breezed through as the seeds escaped unscathed on Sunday.
Two-time Wimbledon champion Kvitova, the 12th favourite in the United Arab Emirates, eased past Italy's Martina Trevisan 6-2 6-1 to make a dominant start.
World number 15 Samsonova was made to work to beat Paula Badosa, winning 6-7 (3-7) 7-6 (7-5) 6-4 to tee up a clash with Qinwen Zheng, who overcame compatriot Zhang Shuai in straight sets.
Samsonova's triumph took three hours and 22 minutes, the longest match of the WTA Tour season thus far, in a thrilling first-round encounter between two top-20 players.
"Playing against Paula is always tough," 14th seed Samsonova said in her on-court interview. "She's doing unbelievable, so I'm really proud that I stayed on the court until the end.
"I think I'm growing match after match, day by day. I know it's a long journey, and I hope to continue like that."
Barbora Krejcikova, the 2021 French Open champion, cruised into the last 32 with a comfortable 6-4 6-2 victory over Irina-Camelia Begu as she aims to go one better than her runners-up finish two years ago in Dubai.
Another routine victory saw American Madison Keys ease past Jasmine Paolini 6-1 6-1, but there was no such luck for 2020 Australian Open champion Sofia Kenin.
She was dispatched 6-1 6-1 by world number 26 Marie Bouzkova, while Amanda Anisimova claimed a 6-3 6-2 win over veteran two-time grand slam finalist Vera Zvonareva.
Viktoriya Tomova had too much for Kaia Kanepi in a 6-3 6-1 success, with her reward a second-round clash against third seed Jessica Pegula.
World number four Pegula lost to the in-form Iga Swiatek in the Qatar Ladies Open final on Saturday, and Leylah Fernandez will face the Pole next after beating Julia Grabher 6-4 6-2.