Peru's champion, which three years ago played in amateur football, made São Paulo surrender with goals from Aldair Rodriguez and Colombian Johan Arango to neutralize Alexandre Pato's goal.
The team from Lake Titicaca was lucky to finish the first half with only one goal against and played comfortably in the second half, when São Paulo was more affected by the 3,800 meters of altitude in the city of Juliaca.
With this result, Binacional, which initially appeared to be the underdog of Group D, finished the first day in second position, behind Liga de Quito, which on Wednesday thrashed River Plate 3-0.
In the first half, the celestial team suffered from inexperience and struggled to stop the Brazilian trident formed by Antony, Pablo, and Pato with only three defenders.
This is how the first goal of the match came, with a goal kick from Volpi that went directly to a three-on-three situation that Pato finished into the net.
The São Paulo team could have gone to halftime with the match decided and a big lead if it weren't for the three clear chances that Pablo missed, one of them with Peruvian goalkeeper Raúl Fernández already beaten.
Until halftime, Binacional barely troubled Volpi except for a shot by Aldair Rodriguez from the edge of the area that the Brazilian goalkeeper deflected for a corner with his fingertips.
The team from Lake Titicaca found the equalizer at the start of the second half, in an isolated play where Rodriguez beat the São Paulo defense and, despite being almost without an angle to shoot, his shot ended up in the net between Volpi's legs, to the delight of the local crowd.
With the new tie on the scoreboard, the extreme altitude began to take its toll on São Paulo, and Binacional took more prominence in attack, increasingly convinced that they could defeat the three-time Libertadores champion, especially with the inclusion of Andy Polar, their most unpredictable player.
Desiring it so much became a reality in the feet of Colombian Arango, who scored Binacional's second goal with a great shot from outside the area after the São Paulo defense gave him all the time to set up the shot. This topped off Binacional's celebration in their first Libertadores match.