The second seed recovered from a 2-5 deficit in the opening set, saving four set points before dominating the tiebreak.
Kalinskaya’s 11 double faults proved costly as Świątek sealed the victory in just under three hours.
Świątek, the 2022 champion, will next face 13th-seeded Russian Ekaterina Alexandrova, who comfortably beat Germany’s Laura Siegemund 6-0, 6-1.
Meanwhile, Poland's Kamil Majchrzak retired from the tournament due to injury in the third round, ending his run following a previous upset victory over ninth seed Karen Khachanov.
(ał)
Source: PAP