The second seed sailed through the opening set but struggled to close out the contest, eventually coming through 6-0 7-6(3).
American Alison Riske relinquished just 14 points on serve as she destroyed Anabel Medina Garrigues 6-0 6-0 while Karolina Pliskova surprised seventh seed Bethanie Mattek-Sands with a 6-2 6-4 victory.
Pavlyuchenkova needed three sets to see off her Italian opponent 1-6 6-4 6-1 while Zakopalova enjoyed a smoother passage after a 7-6(4) 6-2 success.
Top seeds Maria Sharapova, Petra Kvitova, Sara Errani and Angelique Kerber all join the action in the second round after receiving byes.
Pattaya Open results
Karolina Pliskova (Czech Republic) beat 7-Bethanie Mattek-Sands (U.S.) 6-2 6-4
2-Svetlana Kuznetsova (Russia) beat Zhang Shuai (China) 6-0 7-6(3)
Andrea Hlavackova (Czech Republic) beat Estrella Cabeza Candela (Spain) 6-2 6-4
Alison Riske (U.S.) beat Anabel Medina Garrigues (Spain) 6-0 6-0
1-Sabine Lisicki (Germany) beat Donna Vekic (Croatia) 7-5 2-6 6-4
8-Peng Shuai (China) beat Patricia Mayr-Achleitner (Austria) 6-1 7-6(1)
Paris Open results
Klara Zakopalova (Czech Republic) beat Caroline Garcia (France) 7-6(4) 6-2