The Argentine giants suffered their first defeat of the tournament against the hard-working Ecuadorians.
The only goal of the match was converted by substitute Edison Preciado Bravo in the 77th minute.
Boca were without a number of their key players including playmaker Juan Roman Riquelme, and this seemed to affect their game.
They dominated their opponents for long moments of the first half, but although they looked dangerous when moving forward they couldn't penetrate the Cuenca defense.
Boca came closest to scoring with a Pablo Mouche effort, after a quick counterattack.
Cuenca came more into the game as the half progressed, but they lacked the necessary efficiency to pressure the Argentines.
In the second period the game opened up, as both teams went in search of the three points.
As the minutes ticked away Boca seemed to feel the affects of playing at such a high altitude, and they lost their momentum.
Edison Preciado gave Cuenca the three points in the 77th minute when he beat Roberto Abbondanzieri after taking advantage of a lapse of concentration in the Boca defense.
With the win Cuenca climbed into second place of Group 2, while Boca remain top of the group, and will still advance to the knockout phase with a 3-0 defeat to Deportivo Tachira at the Bombonera stadium.
Gregory Sica, Goal.com