Hungarian Czink, who is currently ranked 88th in the standings, began the encounter brightly by holding her opening two service games.
However, the 29-year-old appeared to be powerless to prevent Sharapova from winning the next five games in succession as she took the first set.
Sharapova had by now found her rhythm and won the first two games of the second set without dropping a single point.
Czink finally recorded a point in the next game and she even broke her Russian opponent's serve to reduce the arrears to 3-1 at one stage.
Sharapova eventually regained the initiative though, coming out on top from a number of long rallies to serve out for the match.