The four-time defending New Haven champion breezed past Makarova 6-3, 6-3 in an 81-minute match.
The third-seeded Dane goes on to face 12th-seeded Sofia Arvidsson of Sweden, who dropped American lucky-loser Melanie Oudin 6-4, 6-1.
Also Monday, fourth-seeded Italian Sara Errani advanced with a 6-4, 7-5 decision over American wild card Bethanie Mattek-Sands. Her next opponent will be Spaniard Carla Suarez Navarro, who beat Hungary's Agnes Szavay 7-6 (7-3), 6-4 in a Sunday match.
Seventh-seeded Russian Maria Kirilenko moved on with a 6-2, 6-2 dismantling of Israeli Shahar Peer on the hard courts at the Connecticut Tennis Center.
Other Day 2 winners included American Nicole Gibbs, German Mona Barthel, Olga Govortsova of Belarus, German Andrea Petkovic and Slovakia's Dominika Cibulkova.