Cristian Penilla and Pedro Velasco were on target as league leaders Barcelona accounted for Cuenca at the Estadio Alejandro Serrano Aguilar.
Coming into the fixture with a four-game winning streak, Barcelona were full of confidence and it showed as they took a 19th-minute lead through Penilla.
Velasco sealed the points in the fourth minute of injury time after Barcelona exposed Cuenca on the counter-attack.
Sunday's win opened a five-point lead for Barcelona at the summit following Mushuc Runa's 3-1 loss to rivals Emelec.
Goals from Miller Bolanos and Javier Charcopa gave hosts Emelec a two-goal lead after 61 minutes at the Estadio George Capwell.
Maximiliano Barreiro hit back for Mushuc Runa with 15 minutes remaining, though Angel Mena made sure of the points in the 93rd minute.
After bouncing back from back-to-back defeats, third-placed Emelec are only a point behind Mushuc Runa.
LDU Loja and El Nacional are level on 10 points with Emelec.
Alejandro Villalva cancelled out Julio Ayovi's opener as El Nacional earned a 1-1 draw at home to LDU Loja.
Elsewhere, LDU Quito drew 1-1 against Olmedo after Norberto Araujo equalised seven minutes from time.
Basement side Manta and Deportivo Quito also drew 1-1.
The match between Independiente del Valle and Universidad Catolica was postponed due to the two teams' participation in the Copa Sudamericana.