Williams, a 23-time Grand Slam winner and a former champion in Cincinnati, needed just 65 minutes to dispatch Gavrilova. She’ll face eighth-seeded Petra Kvitova in Tuesday’s second round.
Williams lost to Johanna Konta 6-1, 6-0 in San Jose, California, before withdrawing from last week’s Rogers Cup in Montreal.
Monday’s first full day of main-draw competition opened with 13th-seeded Madison Keys holding off Bethanie Mattek-Sands 3-6, 7-6 (3), 6-4 to reach the second round. Wild-card Victoria Azarenka, a two-time Australian Open champion, also came from behind to beat Carla Suarez Navarro 6-7 (5), 6-2, 6-4.
Tenth-seeded Julia Goerges was losing to Kristina Mladenovic 6-4, 3-2 when she retired because of a lower left leg injury. Advancing were qualifier Ajla Tomljanovic, Aryna Sabalenka, Lesia Tsurenko, wild card Svetlana Kuznetsova, qualifier Viktoria Kuzmova and Anett Kontaveit.
Information from The Associated Press was used in this report.