Desabato, 36, scored in either half against the Ecuadorians as Estudiantes bounced back from last week's 1-0 loss at Independiente, ensuring a 4-1 aggregate triumph.
The emphatic victory at Estadio Ciudad de La Plata means Argentina have another representative in the group stages of South America's premier club tournament, with Estudiantes to come up against Atletico Nacional, Barcelona and Libertad in Group Seven.
Desabato was the unlikely hero for Estudiantes on Thursday, with the five-time Argentina international centre-back opening the scoring in the 13th minute after poking the ball beyond goalkeeper Librado Azcona.
Estudiantes doubled their lead approaching the half-hour mark, when Guido Carrillo headed powerfully past Azcona.
The result was virtually put beyond doubt six minutes into the second half after Desabato glanced a header into the bottom corner of the net at the near post.
Independiente's woes were compounded in the second minute of injury time, when Arturo Mina headed the ball into his own net.
Joining Estudiantes in the group stages are Chilean club Palestino, who edged Nacional 2-2 on away goals.
Palestino were the beneficiaries of the away-goals rule after Thursday's second leg ended 2-1 in favour of Uruguayan hosts Nacional.
Last week's opener was won 1-0 by Palestino.
Palestino have been placed in Group Five alongside Zamora, Boca Juniors and Montevideo Wanderers.
