Jose Salomon Randon scored the only goal of the game in the 14th minute to lift the nation to fifth in the group stage, with Copa America winners Uruguay trailing in sixth and Chile ahead of them on goal difference in fourth.
The Conmebol section has been fiercely competitive and the Vinotinto remain within touching distance of a first-ever finals should their run of results continue, much to the delight of their coach.
"The boys gave everything,” Farias told reporters after the match. “[Oswaldo] Vizcarrondo, [Andres] Tunez, Rincon and [Juan] Arango... they all played through the pain barrier.
"We had so many chances. We had to win the game and we gave Colombia no clear opportunities [to score]. There is no substitute for victory.
"Now an entire country can celebrate knowing that they have a chance to go to the World Cup.
The top four in the South American qualification section qualify outright for the 2014 tournament and fifth place will play-off with an AFC side for a berth, and Farias is more than satisfied with how the group is shaping up.
"We won and the rest is history,” he continued. “I experienced the game as a coach who wants to make it to the World Cup and is proud of his players. I am intensely proud to be Venezuelan and be part of the Vinotinto.
"We Venezuelans represent the Vinotinto. This is Venezuela. We play for Venezuela. We're not imitating anyone."
Argentina currently sit top of the nine-team Conmebol group stage, with Ecuador and Colombia - both with a game in hand on those around them - in second and third respectively.