Third-seeded Robredo won his eight consecutive match in beating Franco Ferreiro of Brazil 6-4, 7-6 (4), while fifth-seeded Acasuso swept aside Oscar Hernandez of Spain 6-1, 6-2.
Robredo leads Acasuso 4-3 in back-and-forth matchup results.
Two weeks ago, Acasuso won their match in Chile then lost in the final. Last week, Robredo won in Brazil and went on to his eighth career title.
On Friday, the Spaniard began to show signs of fatigue against Ferreiro, a qualifier who was playing in his first career quarterfinal. Robredo lost his serve three times and barely won half the points in a match which lasted 1 hour, 50 minutes on the clay.
By contrast, Acasuso took just over half the time to be on the verge of making his third hometown final.
Unseeded Juan Monaco, the hometown champion two years ago, continued to defeat his countrymen, beating qualifier and childhood friend Maximo Gonzalez 6-2, 6-3 after wins over Sergio Roitman and Martin Vassallo Arguello.
Ferrero received a massage at the start of the second set but it was not enough. The former French Open champion had also complained of having a fever for a few days.
Ferrero had difficulty handling Nalbandian's strong service and backhand and the defending champion won the first set with three service breaks to one. It came to a disappointing end soon after, with Nalbandian taking a 4-3 lead in their series.