The 26-year-old former world number one got the better of her Czech opponent 6-4 6-7(7) 6-2 in the third round on Saturday.
Sharapova won the first set 6-4 with a convincing performance, but then struggled to maintain her momentum in the second.
The Russian was 4-1 down at one point, but staged a comeback to take it to a tie-break and earn herself two match points.
However, on both occasions the fourth seed failed to take advantage and was forced into a third and deciding set.
This time, though, Sharapova regained her rhythm, broke early and went on to wrap it up 6-2, taking a total of two hours and 56 minutes to win the match.