In the other semifinal, World number four Karolina Pliskova will be up against the 19th-ranked Czeh Republic Marketa Vondrousova. The two semi-final matches will be played today.
In quarterfinals matches, Halep rolled to a 6-2, 2-0 lead when her Kazakh opponent Yulia Putintseva retired with a back injury while Second seed Pliskova beat Belgian 11th seed Elise Mertens 6-3, 3-6, 6-0.
In other quaterfinal encounters, Muguruza ended the run of US Open finalist Victoria Azarenka 3-6, 6-3, 6-4 while two-time winner Elina Svitolina fell 6-3, 6-0 to Marketa Vondrousova.
In the Men’s Singles category, nine-time Rome champion Rafael Nadal lost to Argentine Diego Schwartzman 6-2, 7-5 in the quarterfinals. World Number 15 Schwartzman will meet Denis Shapovalov of Canada in the semifinals.
In the other match, World Number 1 Novak Djokovic defeated Dominik Koepfer of Germany 6-3, 4-6, 6-3 to earn a spot in the semifinals. Djokovic will meet Norwegian Casper Ruud for a place in the final who beat fourth seed and local favorite Matteo Berrettini 4-6 6-3 7-6(5) in the quarterfinal clash. The two semi-final matches will also be played today.
Earlier, India’s Rohan Bopanna and Denis Shapovalov of Canada bowed out of the Men’s doubles event after losing to the French duo of Jeremy Chardy and Fabrice Martin in quarterfinals.