Makarova piled up five breaks in nine receiving games for a 6-4, 6-2 win. She won nearly half -- 31-of-63 --of the points off Jankovic's serve and was able to finish off five of her 10 break chances.
Makarova did drop her serve twice in an aggressive serving game. She had eight aces but landed just 53 percent of her first serves and had five double faults.
No. 5-seeded Angelique Kerber topped Dominika Cibulkova 7-6 (7-5), 7-5 in a match that took more than 2 hours. Kerber finished with six breaks, four in the second set. Cibulkova had nine double faults against no aces and was good in just 51 percent of her first serves.
Caroline Wozniacki, the No. 6 seed, rallied for a 3-6, 6-2, 6-4 win over Julia Goerges. Goerges dropped only seven points on serve in taking the first set but Wozniacki came back with a pair of breaks in each the second and third sets.
U.S. qualifiers Bethanie Mattek-Sands, Lauren Davis and Christina McHale gained spots in the second round. Mattek-Sands beat Eugenie Bouchard 6-4, 6-3, McHale edged Alize Cornet 6-7 (4-7), 6-2, 7-5 in a 3-hour battle and Davis was a 6-4, 7-6 (10-8) winner over Jarmila Gajdosova. Tsvetana Pironkova, another qualifier, also advanced, posting a 6-4, 6-1 decision over Sorana Cirstea.
Other first-round winners Monday were Carla Suarez Navarro, Kaia Kanepi, Varvara Lepchenko and Lucie Safarova.