Stepanek, seeded fifth, defeated Martin Fischer 7-5, 6-3 despite having his serve broken four times. He survived taking just 53 percent of the points on serve by finishing off seven of his 13 break chances.
Fischer, who fell to 0-3 in main-draw ATP marches this year, had his serve broken four times in the opening set and then managed just one break opportunity in the second set.
Rosol, the No. 8 seed, was on the court 65 minutes in a 6-3, 7-5 win over Jesse Huta Galung. Rosol fired 13 aces and took almost three-quarters of the points on serve. He saved both the break points he faced.
Jo-Wilfried Tsonga, battling for a spot in the ATP World Tour Finals, is the top seed for the tournament.