Stepanek saved two set points while serving at 5-4 down in the opening set. He missed his first match point at 5-4 in the final set before closing out the victory with his 15th ace.
Also, eighth-seeded Lukas Rosol of the Czech Republic served 10 aces while beating Mirza Basic of Bosnia-Hercegovina 6-3, 7-5 to reach his third quarterfinal of the year.
In first-round play, Lukasz Kubot of Poland defeated Florian Mayer of Germany 7-6 (1), 6-4. The 74th-ranked Kubot, who came back from 3-0 down in the second set, next plays third-seeded Fabio Fognini of Italy.