Cesar Gonzalez scored the only goal of the game just after the hour mark, leaving La Vinotinto at the head of the group with four points. Brazil and Paraguay, both with two, trail in their wake after they drew, with Ecuador bottom.
With Ecuador missing Manchester United winger Antonio Valencia with an ankle injury, they were never able to fully get going, unlike their opponents, who had Gonzalez to carry them forward at every opportunity.
Gonzalez gets deserved goal
He had a run and shot after the restart and then, with 62 minutes gone, gave Marcelo Elizaga no chance with a fizzing 25-yard drive after Fedor's cute lay-off.
Fedor looked set to pull the trigger for a second until Norberto Araujo's fine saving tackle, while Arango's stunning run into the box was halted when his team-mates crowded him out.
Felipe Caicedo then had a glorious chance to level for Ecuador, turning his way through traffic to find himself through on Renny Vega's goal, but his six-yard effort was straight at the goalkeeper. Vega then worked harder to keep out Benitez at his near post, but the rally was too little too late for Ecuador.