The Danish former world number one was far from comfortable on her own serve in Yale, but with Makarova struggling even more, she did enough to secure a date with Sofia Arvidsson.
Swede Arvidsson beat home hope Melanie Oudin 6-4 6-1 to book her place in the next round.
Fourth seed Sara Errani won through with a 6-4 7-5 victory over another American Bethanie Mattek-Sands, while numbers six and seven seeds Dominika Cibulkova and Maria Kirilenko also progressed in straight sets.
Cibulkova saw off Anabel Medina Garrigues 7-5 6-3 while Kirilenko eased past Shahar Peer 6-2 6-2.
Up and coming Mona Barthel continued her progression with a 6-3 7-5 win over Daniela Hantuchova, Andrea Petkovic downed Timea Babos and Nicole Gibbs won an all-American clash with Alexa Glatch 6-4 1-6 6-4.
Olga Govortsova of Belarus beat Vera Dushevina 6-7(5) 6-4 6-2; her prize is a second-round clash with top seed Agnieszka Radwanska.