Colombia took seven points from their three matches, the best return of the tournament so far, to qualify for a quarter-final against the best third-placed team from the three groups in Cordoba next Saturday.
Bolivia were eliminated while hosts Argentina and Costa Rica were set to play for second place in Cordoba on Monday.
Falcao put the Colombians ahead after a quarter of an hour when he ran onto winger Dayro Moreno's defence-splitting ball down the left to steer it past goalkeeper Carlos Arias.
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Colombia went further head close to the half hour with a penalty converted by Falcao after defender Santos Amador brought down left back Pablo Armero.
Falcao is now joint top scorer of a low-scoring tournament with two goals, equal with Peru's Paolo Guerrero.
It was the second penalty of the tournament and the second faced by Arias after he saved one from Costa Rica's Joel Campbell in Bolivia's 2-0 defeat in Jujuy on Thursday.
Midfielder Adrian Ramos almost made it three when his header from a perfect high cross from Armero went just over the bar.
Colombia's goalkeeper Luis Martinez had trouble turning away a free kick from midfielder Ronald Garcia near the end of the first half and Jhasmany Campos had a half chance for Bolivia early in the second but his effort went over.
Colombia created several chances to increases their lead with Falcao shooting wide from the best after being set up by substitute Hugo Rodallega, who later had a shot on target deflected by a defender.
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