The world number 12 eased to a 6-4 6-2 victory over the 17-year-old qualifier, who saved five match points in her final service game before Bencic closed things out.
“My love affair with clay is… I’m trying to improve myself on it,” Bencic said after her first-round triumph.
“I think I’m getting better and I’m taking falls sometimes. I’m trying my best on this surface.”
Maria Sakkari was similarly comfortable in progressing to the next round, hitting 24 winners as she dispatched Andrea Petkovic 6-2 6-2 on her debut at the tournament.
At the Istanbul Cup, four of the five scheduled matches were completed before rain stopped play with Anastasia Pavlyuchenkova and Anastasia Potapova level at a set apiece.
Eighth seed Wang Qiang fought back from a set down to beat Anastasia Gasanova 4-6 6-1 6-2.
There were also wins for Ana Konjuh, Katerina Siniakova and Viktorija Golubic.