Osaka made a name for herself by winning a first WTA title at Indian Wells last month and beat Serena Williams in the Miami Open before being her winning run was halted by Elina Svitolina.

The 20-year-old from Japan, up to 21st in the rankings, had no trouble adjusting to playing on the red surface, beating the unseeded Brady 6-4 6-4 on a day which saw US Open champion Sloane Stephens pull out of the tournament due to fatigue following her triumph in Miami.

Osaka struck 22 winners and made only 19 unforced errors, the 10th seed breaking three times to book a second-round encounter with the fit-again Laura Siegemund, who beat Natalia Vikhlyantseva.

Daria Gavrilova, the 11th seed, recovered from a poor start to see off Ons Jabeur 1-6 6-4 6-3, while fellow seeds Kiki Bertens and Alize Cornet defeated Veronica Cepede Royg and Kateryna Bondarenko respectively in straight sets.

Mihaela Buzarnescu was the only other seed in action in South Carolina, the Romanian winning the first set 6-4 before her opponent Vera Lapko retired due to a knee problem.

Sixth seed Ana Bogdan battled back from a set down to beat home contender Victoria Rodriguez 4-6 6-4 7-6 (7-5) in the first round of the Monterrey Open.

Sachia Vickery, Alison Riske, Ajla Tomljanovic, Lesia Tsurenko and Magdalena Rybarikova also progressed on the opening day of the tournament in Mexico.