Bencic will next face qualifier Kirsten Flipkens, who won 6-3, 3-6, 6-3 against the fifth-seeded Dayana Yastremska.
Karolina Muchova followed up her win over Svetlana Kuznetsova by ousting fourth-seeded Donna Vekic 6-4, 6-2 in the second round. She next plays Ekaterina Alexandrova.
In the men's draw, Karen Khachanov saved five match points before winning 3-6, 6-3, 7-6 (7) against the experienced German Philipp Kohlschreiber. Khachanov faced match point at 5-3 and 6-5 in the deciding set, and then again in the tiebreaker.
Khachanov is ranked eighth but faces a plunge in the coming weeks if he can't match the points he won with titles in Moscow and Paris near the end of last season.
Italian veteran Andreas Seppi beat Roberto Carballes Baena 5-7, 6-1, 6-3. The 35-year-old Seppi hasn't won a tour title since the Kremlin Cup in 2012.
Egor Gerasimov beat Thomas Fabbiano 6-3, 6-4.
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