Caroline Wozniacki sealed her spot in the second round of the Ericsson Open with a victory over Pauline Parmentier, while Arina Rodionova ousted defending champion Duan Ying-Ying in the Jiangxi Open on Tuesday.
Top seed Wozniacki, playing her first match since losing to Coco Vandeweghe in the fourth round at Wimbledon, was not at her best back on clay but prevailed 6-3 3-6 6-2 in Bastad.
The former world number one had to come from behind in the first and third sets of a match in which she was broken four times, but came through to set up a meeting with Victoria Golubic.
Third seed Caroline Garcia came from a set down to edge out Irina-Camelia Begu, but Johanna Larsson was beaten on home soil, the Swede losing a third-set tie-break to Mona Barthel.
Kiki Bertens, on a high after winning her second title of the season in Gstaad on Sunday, was a straight-sets winner against Carina Witthoeft, but eighth seed Julia Goerges retired due to injury during her match against lucky loser Viktoriya Tomova.
Duan claimed her solitary WTA singles title in Nanchang last year, but there will be no repeat this week after Rodionova sent her crashing out.
The Australian won 7-5 6-4 and will take on Liu Fangzhou in round two. Jelena Jankovic, the 2015 champion, saw off Kang Jiaqi 6-2 7-5 after bowing out in the first round at Wimbledon.
Wang Yafan and Lu Jing-Jing also advanced to the last 16, but eighth seed Risa Osaki was beaten 6-0 7-5 by Zhu Lin.