Romania's Cirstea reached the second round with a 6-4, 7-6 (7-5) decision over Tatjana Malek of Germany.
Lepchenko, meanwhile, needed three sets to put away fellow American Christina McHale 6-3, 4-6, 6-2 on the green clay at Daniel Island Tennis Center.
Thirteenth-seeded Austrian Tamira Paszek was trailing in her match against American qualifier Grace Min when she retired with an injury.
American wild card Bethanie Mattek-Sands also registered a win Monday, outslugging Anastasia Rodionova of Australia 6-4, 6-7 (4-7), 7-6 (7-3).
Qualifier Mallory Burdette of the United States prevailed over France's Kristina Mladenovic 6-1, 1-6, 6-0, and Olga Govortsova of Belarus bested American Jamie Hampton 6-4, 6-7 (3-7), 6-4 in other Family Circle matches.
Italian Camila Giorgi, Puerto Rico's Monica Puig, France's Mathilde Johansson, Swiss Stefanie Voegele and Canadian qualifier Eugenie Bouchard each posted a Day 1 victory as well.