Stepanek dominated the deciding tiebreaker to reach his first quarterfinal since the clay-court Rome Masters in May.
Stepanek will face Eduardo Schwank, who outlasted Victor Hanescu 7-6 (6), 6-7 (5), 6-3. Adrian Mannarino also advanced with a 6-4, 7-5 win over Rik de Voest.
Mannarino will play either Marc Gicquel or Nicolas Mahut, who played later. Fourth-seeded Paul-Henri Mathieu also played Romain Jouan in another all-French matchup.
Moya, Simon reach BCR Open final
Moya, Simon reach final in Bucharest
Advocaat: We Can Beat Juve & Madrid