Falcao came on in the 78th minute and scored the deciding goal in the second minute of injury time.
Dorlan Pabon gave Colombia a 1-0 lead in the 48th minute and Bolivia's Walter Flores equalized in the 85th.
Colombia coach Leonel Alvarez surprised many by leaving Falcao on the bench and playing most of the match with Teofilo Gutierrez as the lone striker.s
It was also a major victory for Colombia since few visiting teams have much success playing in the thin air in La Paz, which is located at 3,600 meters (11,800 feet).
Bolivia : Daniel Vaca, Lorgio Alvarez (Jose Luis Chavez, 76), Ronald Raldes, Ronald Rivero Luis Gutierrez (Jhasmany Campos, 70), Walter Flores, Jaime Robles, Rudy Cardozo, Pablo Escobar, Juan Carlos Arce, Marcelo Martins (Augusto Andaveris, 70).
Colombia : David Ospina, Camilo Zuniga, Amaranto Perea, Aquivaldo Mosquera, Pablo Armero, Carlos Sanchez, Abel Aguilar, Freddy Guarin (Diego Chara, 70), Dorlan Pabon (Dayro Moreno, 60), James Rodriguez, Teofilo Gutierrez (Radamel Falcao, 78).