Nestor Pekerman's side reached the 27-point mark and secured their place in Brazil next year alongside Argentina, who had already qualified, while Chile will have to wait until the last round of matches.
During the first half, the Cafeteros started better, but Chile began to cause problems on the counterattack and in the 17th minute goalkeeper David Ospina felled striker Eduardo Vargas inside the box. Midfielder Arturo Vidal did not fail from the spot.
Chile took advantage of Colombia's confusion after the goal and five minutes later forward Alexis Sanchez doubled the advantage after great work from playmaker Jorge Valdivia.
Before the half-hour mark, Barcelona's Sanchez clinched the third for La Roja after he connected with Marcos Gonzalez's header near the six-yard box.
Colombia came out fighting in the second half and Chile needed goalkeeper Claudio Bravo to produce a string of saves to preserve their three-goal advantage.
However, in the 65th minute Chile midfielder Carlos Carmona saw his second yellow and three minutes later River Plate forward Teo Gutierrez scored to put his side back in it.
Visiting defender Francisco Silva pushed playmaker James Rodriguez inside the box in the 74th minute and striker Falcao pulled another one back from the spot.
Then with seven to go, keeper Bravo fouled James Rodriguez and Falcao, once again, converted the spot-kick to level the encounter and the the Barranquilla stadium exploded.
In Quito, Ecuador joined Chile on 25 points with a 1-0 triumph against Uruguay which put them on the brink of World Cup qualification.
Ecuador broke the deadlock when a long ball from Manchester United's Antonio Valencia was pushed into the net by Jefferson Montero near the half-hour mark.
It left Uruguay on 22 points and looking at a two-legged play-off against Jordan.
Venezuela's chances of going to Brazil were ended as they drew 1-1 in Paraguay in their final qualifier.
The last round will be played on Tuesday when Uruguay meet Argentina, Colombia visit Paraguay, Chile host Ecuador and Peru face Bolivia.