The fifth-seeded Stepanek beat Martin Fischer of Austria 7-5, 6-3, despite being broken three times in the opening set. He converted six of his own 13 break points in total.
In the only other first-round match, eighth-seeded Rosol had 13 aces in a 6-3, 7-5 win over Jesse Huta Galung of the Netherlands.
The son of 1988 Olympic champion Miloslav Mecir came through three qualifying rounds to earn his first main draw entry. The 25-year-old Miloslav Mecir Jr. of Slovakia, who is ranked 240th, plays Pablo Andujar of Spain on Tuesday.
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