Williams defeated Carla Suarez Navarro,6-3, 3-6, 6-1, in Arthur Ashe Stadium.
Williams next opponent at Indian Wells will be an ascending WTA star, Daria Kasatkina.
The Spaniard is playing on another level, but the Czech has the power to match it.
Can the big Croatian snap his five-match losing streak against the world No. 1?
Fifth-seeded Elina Svitolina rallied from 2-5 down in the third set to beat Petra Martic.