Both teams were in a must-win situation coming into the match, because of their poor form in the qualifiers.
Venezuela, who were thrashed 4-0 by Argentina on Saturday, stood by their game plan, and their persistence paid off as they won the match with two second half goals.
The first half was very entertaining, but it lacked any clear goal-scoring opportunities.
Venezuela tried to inflict pressure in the attack, but they came up against a solid Colombia defense that stood firm at all moments.
In the 27th minute the match changed, as Abel Aguilar reduced Colombia to ten men with his second bookable offense.
This affected the Colombians a great deal, as they struggled to deal with Venezuela's attacks, particularly down both sets of flanks.
After the break Colombia came more into the match, and they dominated Venezuela for large periods.
But Venezuela continued to look more dangerous when moving forward, and they finally broke the deadlock in the 76th when Nicolas Fedor tapped in a cross from the left flank.
The Venezuelans were clearly the better side by this stage, and Juan Arango doubled their lead in the 81st when he curled in a spectacular free-kick that went in off the underside of the crossbar.
Venezuela secured three vital points that see them move within one point of Colombia, who remain in sixth place after twelve rounds.
Gregory Sica, Goal.com