Monaco, the defending champion, defeated Robby Ginepri of the United States 7-5, 7-6 (3) to set up a semifinal match against Ljubicic, who fought off five match points before beating Daniel Gimeno-Traver of Spain 6-3, 4-6, 7-6 (6).
Davydenko twice needed medical treatment for a left thigh injury in the second set, but looked healthy again in the decider against Seppi, who had beaten Dudi Sela of Israel 7-5, 6-1 earlier in the day.
The second round and quarterfinals were played on the same day because of rain disrupted the schedule earlier in the week.
Ljubicic was in control of his match until he dropped serve against Gimeno-Traver on the first break point at the end of the second set.
"All was going well for me, so I lost my concentration a bit," Ljubicic said. "I cannot afford doing that, I have to be sharp to play well on clay."
The 109th-ranked Gimeno-Traver had four match points at 6-5 and one more in the tiebreak, but Ljubicic won on his first match point when the Spaniard netted a backhand.
Monaco dropped serve three times but broke Ginepri four times to clinch the opening set. Monaco converted his first match point in the tiebreak.
Also, Davydenko defeated John Isner of the United States 6-2, 6-7 (6), 6-3. After quickly winning the opening set, Davydenko got into trouble in the second when the 6-foot-10 Isner hit 13 of his 21 aces.
"There was nothing I could do about that, his serve got so strong," the fourth-ranked Russian said. "The rallies were short so it was difficult for me to find my regular game from the baseline."