Argentina, who lead the 10-team round-robin competition, now have 19 points after nine matches.
Colombia, with 16 points, remain second after losing 1-0 at Bolivia on Thursday (Friday AEDT).
The two results momentarily put Brazil out of automatic World Cup berths, in seventh place with 10 points. The Brazilians face Chile in Santiago later on Thursday.
Argentina's lead in the competition could be reduced on Friday if Uruguay, with 15 points, win at Peru.
Defender Nicolas Otamendi opened the scoring for Argentina in the 13th minute. He pushed the ball into the empty net after a cross by Messi and a mistake by goalkeeper Rafael Romo.
Salomon Rondon equalised in the 65th minute with a header for the only South American team yet to play in a World Cup.
""It was an ugly match. We couldn't even make two passes in a row, the ball stopped because of the water on the pitch,'' Messi said after the game.
Argentina's Lionel Messi was not helped by weather conditions in the clash with Venezuela. (AP PHOTO)
"It is difficult to play in these conditions, the pitch did not help.''
Messi returned to the national team after missing the two previous rounds with ligament damage in his right ankle.
Venezuela defender Jon Aramburu said his team wanted a win to show its ambition.
"The rain affected the match, we couldn't play well," he said. "We drew against a team that everyone knows of its potential. But this team is here to beat them, to compete."
Venezuela's next match will be at Paraguay on Tuesday, the same day Argentina host Bolivia.
Colombia, the last unbeaten team in South American qualifying, were shocked at Bolivia in the Municipal Stadium in the city of El Alto, more than 4000m above sea level.
Bolivia moved into fifth place with 12 points after their first win in 21 years against the Colombians.
Miguel Terceros, also known as Miguelito, scored the winning goal for Bolivia in the 58th minute with a powerful shot after dribbling through two defenders.
Bolivia haven't qualified for a World Cup edition since the 1994 edition in the United States.
Colombia's next rival will be Chile, who face Brazil later on Thursday.
Also on Thursday, Ecuador and Paraguay drew 0-0.
The Ecuadorians are in fourth place with 12 points and ahead of Bolivia on goal difference. Paraguay remain out of an automatic qualifying spot with 10 points.
The top six teams in the round-robin competition will secure automatic berths at the 2026 World Cup.
- with Reuter
