The 21-year-old Russian topped Czink 6-2, 2-6, 6-3 and goes on to meet the Taiwan's Kai-Chen Chang in the third round.
Americans Vania King and wild card Coco Vandeweghe also recorded wins at the William H.G. FitzGerald Tennis Center and will meet each other in the quarters.
Fourth-seeded King downed countrywoman Irina Falconi 6-2, 7-6 (7-5) and No. 7 Vandeweghe dispatched France's Aravane Rezai 6-2, 6-2.
Canadian wild card Eugenie Bouchard advanced, rallying to beat eighth-seeded Olga Govortsova of Belarus 1-6, 6-0, 6-3. She goes on to face third-seeded American Sloane Stephens.
Slovakians Jana Cepelova and Magdalena Rybarikova also came out winners on Day 4.