The baseball-loving Venezuelans, once the whipping boys of South American football, have four points having held holders Brazil 0-0 in their opening match in La Plata last Sunday.
Brazil and Paraguay are joint second with two points apiece after a 2-2 draw in Cordoba earlier on Saturday.
Midfielder Cesar "Maestrico" (Little Master) Gonzalez scored the only goal just past the hour when he fired in a shot from outside the box past static goalkeeper Marcelo Elizaga, who was unsighted by one of his defenders.
It was a deserved victory for Venezuela, whose only two previous wins in the competition were on home soil.
President Hugo Chavez, back in Venezuela after undergoing cancer surgery in Cuba, was quick to congratulate Gonzalez on his Twitter account.
"Bravo to our gunner Cesar Gonzalez... that little master," Chavez wrote on @chavezcandanga.
Ecuador, without Manchester United winger Antonio Valencia, who is nursing an ankle injury, squandered several chances to equalise.
Striker Felipe Caicedo dribbled past several defenders in the box but his weak shot easily stopped by keeper Denny Vega.
Another clear chance came when Caicedo passed to Cristian Benitez, who chested down and shot on target, but it was again saved by Vega.
Midfielder Edison Mendez passed to captain Walter Ayovi but he missed probably the clearest opportunity with a left-footed shot over the crossbar.
Elizaga, man of the match when Ecuador held Paraguay 0-0 in Santa Fe last Sunday, saved from Venezuela left back Gabriel Cichero early in the match.
Midfielder Juan Arango, Venezuela's most influential player, had a shot on target near the end of the first half that Elizaga dived to push away.
