Chasing a fourth title of the year and the 50th of her career, Williams had too much power for the slightly-built Dominguez Lino, who nonetheless managed to unsettle her illustrious opponent with some clever drop shots and lobs.
Williams, 31, said she had enjoyed the test and the experience would stand her in good stead the next time she came up against a player like the 47th-ranked Spaniard, who likes to mix up her shots.
"I made a lot of errors, but her game kind of forces you to make errors," the American told a news conference. "It was a really good clay-court tennis match for me.
"Seeing as I have a few more tournaments on clay, it was perfect to play a match like this, so I know if I face another opponent like that I'll have that experience and I'll know how to play."
A 15-times grand slam singles champion, Williams will play unseeded Frenchwoman Kristina Mladenovic or 13th-seeded Russian Maria Kirilenko for a place in the quarter-finals.
Russian second seed Maria Sharapova was due to play her second-round match against American qualifier Christina McHale later on Tuesday. (Reporting by Iain Rogers, editing by Clare Fallon)