The Czech player came out on top in a match that lasted two hours 27 minutes to beat Isner 6-4 6-7 6-3.
Stepanek nullified the threat of the American's serve in the opening set and he took one of his four break-point opportunities to take the set 6-4.
Isner improved in the second set and he sealed the first mini-break of the tie-break to set up a set point, which he duly converted with an ace.
Stepanek broke Isner's serve midway through the deciding set and he created a match point at 5-2, but Isner fought back to hold on to his serve.
However, Stepanek ensured that he did not lose serve throughout the match by serving out the victory in the following game to advance to the last eight, where he will face Andy Murray.