Elina Svitolina made short work of Evgeniya Rodina en route to reaching round two of the Taiwan Open, while Sam Stosur returned to winning ways against Danka Kovinic.
Top seed Svitolina, playing her first match since reaching round three of the Australian Open, needed less than an hour to see off her Russian opponent 6-0 6-3.
Svitolina lost only three points on her own serve during a dominant first set that resulted in a bagel.
And she did not face a break point throughout as she set up a round-two clash against Lucie Hradecka, who overcame Kateryna Kozlova in three sets.
Second seed Stosur, handed a wildcard for the event, suffered a disappointing first-round exit at her home grand slam in Melbourne, but had too much for Kovinic in a 6-2 6-4 win.
Next up, the Australian faces Dalila Jakupovic, who defeated Francesca Schiavone.
Frenchwoman Caroline Garcia, seeded third, also faced little trouble on her way to beating Marina Erakovic 6-3 6-2.
Eighth seed and former world number one Jelena Jankovic was the biggest casualty of the first round as she was sent packing by Kurumi Nara in a 6-7 (4-7) 7-5 6-4 defeat.
Rounding off the action, Lucie Safarova and Peng Shuai won in straight sets against Aleksandra Krunic and Zheng Saisai, while Zhu Lin needed three to see off Magda Linette.