Argentina earlier triumphed 2-1 in Colombia to go level on points with Uruguay, who were not in action, and Cesar Farias' Venezuela joined them on the seven-point mark after defender Oswaldo Vizcarrondo headed home a 25th-minute corner to give the Vinotinto their second win in four matches.
It was a third defeat in four games for Bolivia, who remained bottom of the standings and were unable to repeat the form they showed in a 1-1 draw against Argentina in Buenos Aires on Friday.
Pablo Contreras opened the scoring in the 28th minute by nodding home a right-wing cross from Matias Fernandez, and Matias Campos-Toro came off the bench to double the lead four minutes from time. His shot was deflected into the net by Paraguay midfielder Victor Ayala.
Borghi said: "I'm proud of what the players did. I feel they played for me, for the technical staff and it makes me feel proud."
Paraguay coach Francisco Arce, meanwhile, told reporters in Santiago: "Chile made the most of their goalscoring opportunities. We had some and we could have scored them, but their keeper had a great night."
In Quito, Ecuador overcame Peru 2-0. Cristian Benitez set up Edison Mendez to break the deadlock in the 69th minute, the ball going in via the left post. Benitez lashed home a loose ball two minutes from time to make the points safe.
Ecuador boss Reinaldo Rueda said: "Peru played an excellent match and were aggressive. We could not relax. The players must now keep playing well at their clubs, finish this league in good form and start the new year even better."
Peru stayed on three points from three games and sit second bottom in the standings.