Baltacha was a straight-set winner over Yaroslava Shvedova 6-2, 7-6 (7-5), and now goes on to play France's Virginie Razzano in the second round.
Razzano secured a 6-2, 6-2 decision over Japanese wild card Misaki Doi on the hard courts of the Tennis Center at College Park.
Mirza, meanwhile, was upset by Canadian Stephanie Dubois 7-5, 6-4.
Also Monday, Varvara Lepchenko downed fellow American Sloane Stephens 4-6, 6-4, 6-3, and Britain's Heather Watson prevailed over Eleni Daniilidou of Greece 6-4, 6-1.
Celebrity Families of 2014 [PHOTOS]