Nicolas Fedor, who plays for Salamanca in the Spanish second division, broke the deadlock when he turned in a low cross from Anyelo Pena in the 77th minute, only two minutes after coming on as a substitute.
Four minutes later Arango curled a free-kick in off the underside of the crossbar as the hosts made Colombia pay for their ultra-defensive tactics.
Colombia, who have scored only six goals in their 12 World Cup qualifiers, had midfielder Abel Aguilar sent off in the 27th minute for a violent lunge at Alejandro Moreno.
However, it made little difference as they were incapable of putting any sort of attacking moves together before or after his dismissal.
The win left Venezuela with 13 points from 12 games in the 10-team group, one behind Colombia, three behind fifth-placed Uruguay and five behind fourth-placed Brazil.
The top four teams qualify directly for the 2010 World Cup in South Africa and the fifth play off against the fourth CONCACAF team. Uruguay visit Chile on Wednesday while Brazil host Peru.
Venezuela's chances nearly all came from Arango's left foot.
The captain was close three times in the first half, all from outside the penalty area, and missed a sitter midway through the second when he side-footed across the face of goal from a free position.
