They finished their rivalry through the Latin American clay-court swing at 2-2, although Robredo still leads 5-4 overall.
The No. 3 seed was on a 12-match winning streak after beating Acasuso in the semifinals en route to titles in Brazil and Argentina in the last two weeks.
Meanwhile, top-seeded Venus Williams and defending champion Flavia Pennetta remained on course to meet in the women's final. Williams overcame a mid-match stumble to put away Hungarian qualifier Agnes Szavay 6-2, 5-7, 6-1.
Coming off her win in Dubai last weekend, Williams has had to sweat through three consecutive three-setters against past winners of clay-court titles to make the semifinals, where she'll play unseeded Barbora Zahlavova Strycova. The Czech was also busy, taking nearly three hours to defeat Maret Ani of Estonia 4-6, 7-5, 6-1.
On Thursday, Acasuso broke the Spaniard to clinch the first set without offering Robredo any break points and then raced through the second.
Vassallo Arguello beat qualifier Dan Koellerer 6-3, 7-6 (6) to reach his first semifinals in two years.
Almagro had 14 aces, gave away only nine points in 10 service games and gave Gimeno-Traver no break chances. Almagro took both of his break points in the first set then needed the tiebreak to fend off 89th-ranked Gimeno-Traver.
In the women's draw, second-seeded Pennetta maintained her bid for a sixth successive final in Acapulco by overcoming Petra Cetkovska of the Czech Republic 2-6, 6-3, 6-0. The Italian improved her record in Acapulco to 27-4.