The No.1-seeded Williams dropped serve once in the second set but converted on all six of her break opportunities to roll over the No.5-seeded Domínguez Lino in a 62-minute straight-setter, 61 61.
"My opponent today was playing really well, so I had to be patient and stay out there as long as I could," Williams said. "I'm getting more used to the clay again. It feels a little better now. I want to play two more matches and win on the last day, but I have a really tough opponent coming up."
Williams' next opponent is indeed one of her toughest match-ups - Klara Zakopalova, seeded No.3 here, cruised past Dutch qualifier Richel Hogenkamp in her quarterfinal match earlier in the day, 62 63.
"Well, the score looks easy but it was not an easy match because it was windy, and the wind was changing a lot," Zakopalova said. "But she was a young and talented player. I never played against her but my coach was watching her so I knew some things, and I'm really happy I'm through today."
Williams leads Zakopalova in their head-to-head, 3-1, but while Williams won their first two meetings handily during the 2003 season, they went 1-1 in their last two meetings during the 2009 clay court season, Zakopalova winning in the first round of Marbella and Williams winning in the first round of the French Open (and it was an incredibly dramatic win - Williams missed out on five match points in the second set and another three in the third set before finally closing it out on No.9, 63 67(7) 64).
"Well, she's the best player in the world," Zakopalova said. "I played against her four or five times before, so I know how she plays, but she's even more experienced now, and she has won so many Grand Slams, so she's really the best. She's playing so well and really deserves to be No.1.
"I know some things, though. I have to move her as much as I can. My serve has to be more solid than it has been. I'll just give my 100%. I have nothing to lose. Playing these matches is like a reward for all the hard work you do - to play against the World No.1 at such a nice tournament is like a present."
What about that win in Marbella? "I remember she was just coming from Miami and was a little bit tired and injured," Zakopalova said. "It's not like the Serena today. She's playing amazing tennis."
The other two quarterfinals saw No.8 seed Johanna Larsson beat Mathilde Johansson, 61 62, and Flavia Pennetta beat Virginie Razzano, 61 63. Pennetta beat Larsson in their only previous meeting.
Both Larsson and Pennetta are through to their third semifinals at this International-level event - Larsson is 1-1 in her previous two semifinals (reaching the final in 2011 and falling in the semifinals in 2012) while Pennetta is 0-2 in her previous two (falling in the semifinals in both 2009 and 2010).