[2] Avilán was handed his first team debut by Uruguayan manager Roberto Scarone in 1964 against Club Deportivo Nacional, helping Monterrey to a 2–0 win.
[2] He was called up to the Mexico national football team on several occasions, making two appearances between 1971 and 1972.
[2] Avilán returned to Monterrey at the end of the 1970s, initially managing the youth sector, which included future Mexican internationals Francisco Javier Cruz, Héctor Becerra and Missael Espinoza.
[2] With signings such as Guillermo Muñoz, he led Monterrey to the México 86 title, the first in the club's history.
The scandal, known as Cachirules, saw several Mexican officials banned from football for life; however, Avilán himself received no sanction, and said that if he had known these players were overaged, he would not have selected them.