The fifth-seeded Peer breezed into the third round, posting a 6-1, 6-3 decision over Sweden's Sofia Arvidsson.
Wickmayer likewise had little trouble advancing, downing China's Jie Zheng in straight sets, 6-4, 6-0, on the green clay courts in Charleston, S.C.
Also moving on in Tuesday's play were No. 11 Peng Shuai of China, who bested Japan's Ayumi Morita 6-2, 6-1, and Chanelle Scheepers, who got past Jill Craybas by a 6-3, 6-2 score.
Twelfth-seeded Julia Goerges moved on when Czech qualifier Eva Birnerova retired in the third set while leading 1-6, 7-5, 2-0.
No. 8 Russian Alisa Kleybanova, meanwhile, fell to 18-year-old American Christina McHale 6-1, 6-0.
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