Schmiedlova, seeded eighth, needed only 44 minutes to complete the 6-0, 6-0 rout of Irina-Camelia Begu. She dropped just three points on serve and 10 overall in the first set and nine in total in the second.
Schmiedlova won 24-of-30 points on serve and 72 percent of all the points.
It was the second "double-bagel" of the tournament. Petra Martic took out Vera Dushevina 6-0, 6-0 in Tuesday's first-round play.
No. 3-seeded Zhang Shuai stopped Julia Glushko 6-2, 6-2 in just an hour. Zhang won more than half (26-of-51) of the points off Glushko's serve and finished off all four of her break chances.
Anna-Lena Friedsam pulled off a 6-4, 6-4 upset of seventh-seeded Ajla Tomljanovic by holding off all five of the break chances Tomljanovic had on the day.
Zheng Saisai came away a 6-3, 6-1 winner over Alla Kudryavtseva in her second-round match. She had one break in the first set and four in the second.