Venezuela had beaten Argentina only once in 14 previous World Cup qualifiers and their hopes of doing it again on Thursday were snuffed out when Luis Adrian Martinez was shown a straight red card for a foul on Lionel Messi after half an hour.
With a man advantage the visitors had most of the ball in the second half and added two more goals in the 71st and 74th minutes through substitutes Joaquin Correa and Angel Correa.
Yeferson Soteldo scored a consolation penalty for Venezuela in stoppage time.
"I think we had a great first half, even before they were left with a man less," said striker Martinez. "After the goal we had more space to work in and we are taking all three points home."
Messi started his first match since the final of the Copa America on July 10 and his flicks and jinks frequently ended with him being fouled as Venezuela struggled to contain him.
Messi, who has played just 24 minutes this season with his new club Paris Saint-Germain, was on the field for the whole game and only some fine saves by Wuilker Farinez kept his name off the scoresheet.
Argentina are second in the 10-team South American qualifying group for next year's World Cup behind Brazil, who beat Chile in a later game on Thursday.