Juan Arango twice put Venezuela ahead while Javier Hernandez and Giovani dos Santos replied for Mexico, whose players had threatened to boycott the game after being fined over a late-night party.
Venezuela defender Gabriel Cichero was sent off after 24 minutes of Tuesday's match in the border town of Ciudad Juarez for a second yellow card.
Mexico's problems began in September when 13 players were disciplined by national teams director Nestor de la Torre for holding a party at the team hotel after a friendly against Colombia in Monterrey.
Carlos Vela and Efrain Juarez were suspended for six months and the other 11, including Manchester United's Hernandez, team captain Rafael Marquez and Dos Santos, were each fined 50,000 pesos ($3,900).
The 13 players asked not to be picked again until De la Torre was removed from his post. Despite this, most of them were included in the squad for Tuesday's match and warned they could face stiffer penalties if they ignored the call-up.
The players travelled for the match and De la Torre quit following a meeting on Monday.
Borussia Moenchengladbach's Arango put Venezuela ahead after only seven minutes with a well-placed shot which left goalkeeper Guillermo Ochoa stranded.
Hernandez headed Mexico level just after the half hour only for Arango to strike again with a shot from outside the penalty area in the 40th minute.
Mexico dominated the second half and levelled when Pablo Barrera slipped the ball to Dos Santos, who scored with an angled shot in the 61st minute.
It was Mexico's last match under interim coach Efrain Flores.
They are due to name a coach later this month with Victor Manuel Vucetich and Jose Manual de la Torre the only candidates.
