Safin, once ranked No. 1 in the world, beat Robredo for the fourth time in six encounters, 7-6 (7-2), 2-6, 7-6 (7-5).
The 24-year-old Safin will play Irakli Labadze of Georgia in the semifinals.
Labadze advanced in a walkover against Spain's Rafael Nadal, who had to withdraw because of a small fracture in his left ankle.
On the women's side, Iveta Bensova of the Czech Republic, Frenchwoman Stephanie Cohen-Aloro, Marta Marrero of Spain and Emile Loit of France reached the semis.