Ecuador, who had taken only a point from their previous two games, proved too strong for a Venezuela side buoyed by a 5-0 win over Bolivia last week.
Arturo Mina headed Ecuador ahead in the 51st minute before the hosts cut loose in the final 10 minutes as Venezuela swarmed forward in search of an equaliser.
Miler Bonanos tapped in from close range to complete a sweeping Ecuador counter-attack and make the game safe on 82 minutes.
Four minutes later it was left to Everton's Enner Valencia to apply the coup de grace, finishing calmly past Daniel Hernandez to make it 3-0 after Venezuela were left exposed at the back once more.
The win sees Ecuador move into third place in the South American standings with 20 points from 12 games.
Uruguay, who play Chile later Tuesday, are second with 23 points while Brazil lead the standings with 24 points from 11 games.
Brazil play Peru in Lima later Tuesday.
In Tuesday's early game, Paraguay's hopes of battling into the top half of the table suffered a setback with a 1-0 defeat against Bolivia in La Paz.
A Gustavo Gomez own goal in the 78th minute secured all three points for Bolivia, who moved off the bottom with the win.