[1] Two years later he transferred to San Lorenzo de Almagro, scoring 34 goals in his first two seasons combined, that being the first of the four spells with the club in an 18-year career.

Acosta spent the following three years out of Argentina, starting and ending with Club Deportivo Universidad Católica in Chile where he rejoined former San Lorenzo teammate Néstor Gorosito.

He added 14 the following campaign, but was deemed surplus to requirements after the signing of Mário Jardel, and returned to San Lorenzo for the fourth and last time, netting always in double digits until his 2004 retirement at the age of 37.

In the 2007 summer he returned to his country, joining fourth division team Club Atlético Fénix's coaching staff and coming out of retirement for a few months.

In the 1993 edition in Ecuador, he converted his penalty shootout attempts in both the quarter-finals and the semifinals, as the nation eventually emerged victorious.