Gajdosova, who picked up her first WTA title at this event last year and is seeded No. 2 this year, raced past Han Xinyun 6-2, 6-1 in 54 minutes. Gajdosova won nearly two-thirds of the points in the match and piled up six breaks in Han's eight service games.
Top-seeded Maria Kirilenko advanced to the second round with a 6-4, 6-2 win over Alona Bondarenko. Kirilenko dropped serve three times but countered by winning 58 percent of the points when receiving serve and ending up with six breaks.
Chan Yung-Jan moved into the next round when No. 3-seeded Ksenia Pervak, three days removed from a tournament win in Uzbekistan, retired from the match. Chan was up 4-1 when play stopped.
Fifth-seeded Bojana Jovanovski joined Pervak on the sidelines after Tetiana Luzhanska posted a 6-3, 4-6, 7-6 (7-4) win and Zheng Jie ousted No. 6-seeded Alberta Brianti 7-6 (7-3), 6-4 in the day's other upsets.
No. 7-seeded Chanelle Scheepers defeated Anastasija Sevastova 7-5, 1-6, 6-3 and eighth-seeded Magdalena Rybarikova outlasted Jill Craybas 6-3, 4-6, 6-2.
Other first-round winners Tuesday were Iryna Bremond, Zhao Yi-Jing, Hsieh Su-Wei, Zarina Diyas, Aravane Rezai and Mandy Minella.