Along with a brief spell with the Mexico national football team Héctor Sanabria played for the UNAM Pumas as a defender from 1965 until 1978. With the Pumas Sanabria won the Copa México and the Campeón de Campeones tournaments in the 1974–75 season, followed by the league title in 1976–77. He played in the football tournament at his home Olympics in Mexico City in 1968 where the national team finished fourth. After his playing career Sanabria became the manager of the Pumas in 1987–88, before leading Deportivo Toluca F.C. to victory in the Copa México the following season.