Cabanas brace brings respite for America
Diaz started the championship in danger of losing his job after Mexico's richest team failed to qualify for the knockout stages of the previous tournament and also missed out on a place in the South American Libertadores Cup.
America were in more trouble when Juan Pablo Rodriguez fired Santos Laguna ahead with a 44th-minute penalty in Sunday evening's match.
But Paraguay striker Cabanas levelled in the 63rd minute when he headed in a cross from new signing Jean Beausejour and then fired the winner with 10 minutes left after another chance created by the Chile forward.
Defending champions Toluca were held to a 3-3 draw at home by Atlante after squandering a two-goal halftime lead and then missing a late penalty.
Mexico midfielder Antonio Naelson put the Red Devils ahead after 17 minutes only for Gabriel Pereyra to equalise four minutes later.
Hector Mancilla scored twice in three minutes before halftime to put Toluca in control but Atlante replied through Pereyra and Luis Gabriel Rey early in the second half.
Toluca's frustration was complete when Carlos Esquivel had an 80th-minute penalty saved by Federico Vilar.