Reinaldo Rueda's side dominated the contest at Olimpico Pedro Ludovico in Goiania but failed to find a way past Venezuela's hardworking keeper.
Rueda restored Duvan Zapata and Luis Muriel to his starting line-up but the duo were frustrated as Colombia attempted 12 first-half shots without success.
The introduction of Porto winger Luis Diaz did little to improve their prospects, and he was shown a straight red card in stoppage time as Venezuela battled to a valuable point.
Yerry Mina should have opened the scoring when he stretched to meet Daniel Munoz's cross after 13 minutes but could not poke the ball into the gaping net.
Colombia continued to press and Edwin Cardona drew a good save from Farinez with a low drive from the edge of the box, and Zapata was denied in a one-on-one moments later.
Zapata burst through a line of Venezuela defenders 10 minutes before the interval but his fierce angled shot was parried away well by Farinez.
Farinez's determined display continued in the second half, when he made a fingertip save to push Mateus Uribe's spectacular overhead kick over the crossbar. The goalkeeper made eight saves in total.
The game became fractious as both sides tired, and Diaz was shown a straight red card after a clash with Francisco La Mantia, compounding Colombia's frustration.