Talavera started his career at Nacional of Barrio Obrero before moving to Club Guaraní where he played briefly. His career advanced in 1971 when he joined Cerro Porteño and won three national championships in a row. In 1975 he moved to rival club Olimpia where he became a key player by winning several national and international titles until 1985, the year of his retirement. Talavera also played for Argentine club Newell's Old Boys.
After retiring from football, Talavera briefly acted as Olimpia's head coach in 2005.