Venus Williams launched a challenge but the 36-year-old American could not get past third-seeded Garbine Muguruza of Spain, who recorded a 6-2, 3-6, 6-2 victory on Friday in the quarterfinals of the Internazionali BNL d'Italia in Rome.
Currently ranked No. 7 in the world, Muguruza will move into the top five when the new rankings are released next week. That means she will get a top-four seeding at Roland Garros when she attempts to defend her French Open title.
Muguruza bolted to an early 4-0 lead on her way to winning the first set as the ninth-seeded Williams committed numerous errors.
Muguruza committed just eight unforced errors in the first set, but had 20 in the second, helping Williams even the match.
Muguruza lost her serve early in the third set, but broke right back and controlled the rest of the match as she got to the semifinals in Rome for a second straight year.
Muguruza's semifinal opponent will be eighth-seeded Elina Svitolina of the Ukraine, who upset second-seeded Karolina Pliskova of the Czech Republic 6-2, 7-6 (9).
Svitolina had lost her last four matches against Pliskova, but turned the tables this time, overcoming a 5-3, second-set deficit, then surviving three set points against her in the tiebreaker to pull off the upset.
"I was very happy today, not even just that I won this match but with the way I played and how I handled the pressure," Svitolina told WTA Insider. "Especially in the tiebreak, the way I handled everything. It was something for me to be really proud of.
"She had a lot of set points and she had been serving for the set. I was just trying to stay in the zone and not think about what's going to happen. I couldn't even believe it when I finished in two sets, I was so into the moment. I'm proud of how I handled the pressure."
The other semifinal will match Romanian Simona Halep against 15th-seeded Kiki Bertens of the Netherlands.
Halep ended the surprising run of qualifier Anett Kontaveit of Estonia with a 6-2, 6-4 victory.
The 21-year-old Kontaveit has beaten Angelique Kerber and Mirjana Lucic-Baroni this week, but could not get past the sixth-seeded Romanian.
Bertens eliminated another qualifier, Daria Gavrilova of Australia, 6-3, 6-3.
"Today was special because this was the first match where I was really calm," Bertens told WTA Insider after the win. "I stayed really calm and focused, and this was the first match where I really had confidence in myself. It felt great.
"It's tough, because coming into the match you always know something is going to happen (when you play against Dasha). You have to be prepared for a long match and I think I was ready for it today, trying to play aggressive. I think that worked well today, and it wasn't too long."