The French Open junior champion is playing on a wild card at her home event and next faces Anett Kontaveit of Croatia.
"I resolved not to make too many mistakes, and was focused on what I had to do. I realized what she was doing to me; she was playing a lot to my backhand, and I had to play to her forehand," said Masarova.
"It wasn't about winning the point anymore, it was about not missing. But when I had the opportunity to make a point, I did."
"A couple points, and it could have gone either way. I wasn't the luckiest, either," Schnyder told wtatennis.Com.
"But we also have to talk about how tough it was to wait with the rain and to play in that wet and cold weather. It was a struggle for both, I know, but for my game, it's helpful when the ball bounces high and it's not too heavy. Normally I'd find these conditions in Gstaad, but not with the rain.