Goalkeeper Wuilker Farinez made a string of fine saves, particularly in the closing stages, to keep out the Colombians, who saw a late Miguel Borja goal ruled out for offside.
Colombia also finished the game with 10 men after Luis Diaz was sent off deep into injury time.
Earlier, Venezuela's Jose Martinez got away with a yellow card after striking Mateus Uribe -- who was also booked for protesting -- in the face, although he was not looking at the Colombian when he did so.
Colombia finished the game with 23 shots to just two -- including none on target -- from Venezuela but the "Red Wine" held out for a much needed point.
Venezuela were still severely depleted from a Covid outbreak in their camp that deprived the team of eight players in their 3-0 defeat to hosts Brazil on Sunday.