Juventus midfielder Arturo Vidal and Eduardo Vargas of Napoli struck after the break at the Estadio Nacional on Thursday.
Vidal broke the deadlock in the 67th minute, converting a spot-kick after he was fouled by Miller Bolanos.
Vargas, who replaced Jean Beausejour at half-time, added a second goal in the 84th minute with a curling effort underneath goalkeeper Alexander Dominguez.
The tournament hosts dominated the encounter from the onset, with Ecuador offering little threat going forward.