Vidal scored from the penalty spot in the 67th minute after being pulled down by Miller Bolanos before Vargas latched on to a pass from Alexis Sanchez to double Chile’s lead with a low right-foot shot six minutes from time.
Ecuador’s best chance came from an Enner Valencia header that bounced back off the crossbar with the score still at 1-0.
Despite their victory, the Chileans created very little for much of the tie and will need to improve if they are realise their hope of a first Copa America title at the 37th attempt.