The Chivas came from behind to score twice in the dying minutes at their Omnilife stadium on Saturday and climb into mid-table comfort after their worst start to a championship.
Club owner Jorge Vergara turned to Dutch great Cruyff after Guadalajara, holders of a record 11 league titles, had picked up only two points in their opening seven matches after losing the first four.
Argentine striker Emanuel Villa put Cruz Azul ahead midway through the first half with a header from the rebound after goalkeeper Luis Michel had parried a stinging shot from midfielder Christian Gimenez.
Guadalajara equalised in the 88th minute when a shot from striker Erick Torres took a deflection on defender Nestor Araujo and left goalkeeper Jesus Corona wrong-footed.
They won in added-time with a penalty converted by captain Hector Reynoso after Araujo had head-butted Torres and been sent off.
"That's three rounds where we have played with heart and soul, we're finding the results and the support of our fans," forward Marco Fabien de la Mora told reporters.
"There's still a long way to go in the tournament and we're on our way back."
Guadalajara are 11th in the standings with 11 points from 10 matches, nine points behind joint leaders Santos Laguna and Morelia.
After the 17-match league phase, the championship moves into the knockout rounds involving the top eight teams with Guadalajara now four points from a place in the quarter-finals.
Guadalajara are looking to boost their youth scheme with Cruyff's help and former Manchester United and Netherlands goalkeeper Edwin van der Sar could join the project.
"I've spoken about it with people close to him. The plan is to bring several assistant coaches to work in the Chivas junior ranks and be able to change several things to reach a higher level. I might like to do that," Van der Sar was quoted as saying by the Mexican daily El Universal.
