The New Zealand No 1 went into the US$795,000 clay court event in Charleston, South Carolina, on the back of consecutive first-round defeats at Indian Wells and Miami but beat Hantuchova 7-6(2) 6-4 in one hour and 50 minutes.
Stosur, the world No 9, is the third seed at the tournament behind Serena Williams and Caroline Wozniacki and easily beat Erakovic in their only meeting in Seoul five years ago 6-2 6-0.