The 15th-ranked Czech next plays qualifier Vincent Spadea of the United States, who beat wildcard Alexander Slabinsky of Britain 6-1, 7-5.
Fifth-seeded Gilles Simon of France ousted American Donald Young 6-1, 6-4, and eighth-seeded Gael Monfils of France defeated Australian Chris Guccione 7-6 (4), 6-4.
In other first-round matches, Thomas Johansson of Sweden went through when qualifier Kei Nishikori of Japan retired after losing the first set 7-5, and qualifier Samuel Groth of Australia beat wildcard Jamie Baker of Britain 7-6 (7), 6-3.
US CLAIM CURTIS CUP VICTORY
Pliskova, Vinci advance to Prague Open quarterfinals
Gonzalez wins at BMW Open; Kohlschreiber out
