Universidad Chile overcame The Strongest for their first win in Group Four, while Juan Aurich were the only other winners on Thursday.
Quick-fire goals from Sebastian Ubilla and Gustavo Canales lifted Universidad Chile to their first victory in the group stages of the Copa Libertadores this season, a 3-1 win at home to 10-man The Strongest.
Universidad Chile came into Thursday's home fixture on the back of successive Group Four losses against Internacional (3-1) and Emelec (1-0).
But the Chilean giants finally opened their Libertadores account thanks to Gustavo Lorenzetti, Ubilla and Canales at Estadio Nacional Julio Martinez Pradanos in Santiago.
Universidad Chile were forced to do it the hard way, though, after Pablo Escobar gave the Bolivian visitors a 17th-minute lead via a curled effort beyond goalkeeper Johnny Herrera.
The hosts hit back three minutes later courtesy of Argentinean midfielder Lorenzetti, who fired a half-volley into the bottom corner of the net from the edge of the penalty area.
The Strongest were reduced to 10 men in the 55th minute when Walter Veizaga saw red for a second bookable offence.
And Universidad Chile took full advantage with Ubilla heading his team in front in the 71st minute before Canales sealed the points seven minutes later.
Universidad Chile and The Strongest have both collected three points from as many games in Group Four, three less than Emelec and International.
Juan Aurich also notched their first win in Group Six after they saw off San Jose 2-0 in Chiclayo, Peru.
Beaten 3-0 by Tigres UANL in their group opener almost three weeks ago, Juan Aurich responded in convincing fashion at home to the Bolivian club.
Cesar Valoyes opened the scoring for Juan Aurich in the sixth minute, blasting the ball into the roof of the net from the edge of the area.
Christian Ramos doubled the lead in the 23rd minute after the poking the ball past Carlos Lampe following a goalmouth scramble.
Juan Aurich are level on three points with San Jose from two games but adrift on goal difference.
As for Argentinean champions River Plate, they collected their first point after playing out a 1-1 draw at home to Group Six leaders Tigres.
Meanwhile, Atletico Nacional drew 1-1 with Estudiantes in Group Seven.