Substitute Angel Sepulveda also scored twice in the final quarter of an hour for Morelia, who ended the match with nine players having fought back from three goals down, but could not prevent Santos from going through.
The aggregate score of the semi-final tie was 4-4 after Morelia won the first leg 2-1 at home in midweek but Santos qualified by virtue of having finished higher in the league standings before the knockout phase.
Looking for their first title since the 2008 Clausura, Santos took the lead just past the half-hour when defender Joel Huiqui brought down Oribe Peralta and midfielder Juan Rodriguez converted the penalty sending Morelia's goalkeeper Federico Vilar the wrong way.
Huiqui was sent off, leaving Morelia a man short for nearly an hour and Santos went further in front early in the second half when Peralta dribbled past three defenders on a run across the edge of the box laying off to Suarez who fired past Vilar.
Suarez scored again in the 65th minute before Morelia, looking no more tired than their opponents despite having been a man short for most of the match, staged a thrilling comeback.
Sepulveda put Morelia back into the match in the 74th minute when he headed home from midfielder Edgar Lugo's cross.
With three minutes remaining, Sepulveda chested down a high ball into the box with his back to goal and a defender breathing down his neck and, as he fell backwards he managed an overhead-kick past advancing goalkeeper Oswaldo Sanchez.
Morelia had midfielder Aldo Ramirez sent off in stoppage-time for a dangerous tackle on Colombian forward Darwin Quintero.
