Nalbandian, who is ranked 11th, took two hours and 43 minutes to win the match 3-6, 7-6 (7-5), 6-4.
The Cordoba-born player started hesitantly and a series of unforced errors cost him the first set.
Unseeded Acasuso could scent victory when the second set went to a tie-break, but Nalbandian drew on his experience to get out of trouble.
"Winning at home for the first time is very special," Nalbandian said. "I made some mistakes early on and winning that second set provided the key. I'm very happy."