In her first tournament since regaining the number one ranking, Williams is trying to win her sixth Sony Open which would break the five titles she shares with Steffi Graf.
"I don't think it was too much rust," Williams said. "I think I missed a few shots, but only because I was off footwork-wise. It's always just good to win a match and stay in the tournament and keep going."
Sloane Stephens came back from a devastating slow start to overcome Olga Govortsova of Belarus 0-6, 6-4, 6-4. Stephens, ranked 16th, is the second highest ranked American after Williams.
"I wasn't playing that great," Stephens said. "I was asleep out there. I definitely just needed to wake up and start playing. A lot just battling and just hanging in there."
Others moving onto the third round of the Sony Open include defending champion Poland's Agnieszka Radwanska,Former French Open champion Li Na and former world No. 1 Caroline Wozniacki.