Substitute Rodrigo Ramallo scored with a diving header from a corner in the 91st minute as the Bolivian side came from behind to beat three-times champions Santos in the Group One match at high altitude in the Hernando Siles stadium.
Midfielder Henrique put Santos ahead in the 10th minute when he scrambled the ball home at a free-kick but Ernesto Cristaldo equalised just past the half-hour mark with a low shot inside goalkeeper Rafael's right-hand post.
Also on Wednesday, Corinthians had been staring at a surprise defeat at Venezuela's Deportivo Tachira in Group Six but equalised when Ralf headed home a free-kick in the fourth minute of added-time.
Forward Sergio Herrera put Tachira ahead with his chest midway through the first half from a failed Corinthians clearance and as the three minutes of added-time ebbed away Alex curled a free-kick into a packed box where Ralf rose to send a bullet header past Robert Rivas for the equaliser.
Another Brazilian side, Flamengo, were held 1-1 by Lanus in Buenos Aires in Group Two.
The visitors went ahead in the first minute of first-half added time when left-back Junior Cesar's low centre evaded a pair of Lanus defenders and Leo Moura fired the ball into the roof of the net.
Lanus equalised with 15 minutes left when Silvio Romero crossed from the right and striker Mariano Pavone turned the ball back inside for substitute Cesar Carranza to blast home.
