San Luis finished level on eight points with Peru's Universitario in Group Eight but edged into second place by a difference of one goal.
The Peruvians lost 2-0 away to eliminated San Lorenzo after also scoring in injury-time, only to see their effort controversially disallowed.
Colombian Jairo Patino put San Luis ahead in the 58th minute in Asuncion and Jose Reyes headed the decisive goal in the 91st minute.
Libertad, who had already qualified, finished top of the group with 12 points.
Peru captain Nolberto Solano started on the bench for Universitario, who fell behind in Buenos Aires when striker Ronaille Calheira turned the ball into his own goal in the 22nd minute.
Alejandro Gomez scored a second to give San Lorenzo's new coach Diego Simeone his first win.
Solano came on at halftime but had to go off injured 20 minutes later.
Piero Alva had the ball in the net for Universitario in injury-time but his effort was ruled out of offside.
Universidad de Chile went through from Group Seven after winning their last game 2-1 away to Bolivian champions Aurora, who lost all six games.
Juan Gonzalez headed the winner for Universidad who leap-frogged Boyaca Chico into second place after the Colombian side lost 3-0 away to Gremio in Brazil.
Gremio topped the group with 16 points out of a possible 18. Despite their performance, coach Celso Roth was fired earlier this month because of bad results in a Brazilian regional competition.
