Djokovic holds a 13-1 career record over the 38-year-old Stepanek, and has won their last 12 meetings.
Djokovic took a 4-2 lead in the first set before Stepanek broke his serve when the second seed netted a backhand on a third break point in the game.
Djokovic won the next two games, winning the set on an overhead smash to an open court.
In the second set, Djokovic established a 3-1 lead and held on to the advantage.
He will play Spaniard Fernando Verdasco in the semifinals. Verdasco defeated sixth-seeded Ivo Karlovic of Croatia 6-2, 7-5.
Top-seeded Andy Murray plays Nicolas Almagro of Spain in the first evening match, followed by third-seeded Tomas Berdych and fifth-seeded Jo-Wilfried Tsonga.
Original author: Ashley Ndebele