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Central Córdoba has played at the highest level of Argentine football on 2 occasions, more specifically in the 1967 and 1971 Nacional championships. In the 1967 Nacional, Central Córdoba finished 14th of 16 teams, having reached its peak with the 2–1 victory over Boca Juniors in La Bombonera.

In 1971 Central Córdoba finished 13th out of 14 teams in group B, with their most significant achievement being a 1–1 draw to Boca Juniors, although soon later the team would be heavily defeated at the hands of San Lorenzo by 7–1.

On 8 June 2019, Central Córdoba won promotion to the Primera División after defeating Sarmiento in the 2018–19 promotion play-off finals. It marked their return to the top-flight for the first time in 48 years. In their first season back they finished 18th in the table.

The club made the final of the 2018–19 Copa Argentina for the first time in its history. They kicked off their run while still in the Primera B, beating Nueva Chicago 1–0, in the round of 32 they beat All Boys by the same score, then beat Villa Mitre to set up a quarter-final with Estudiantes de La Plata, winning 1–0. In the semi-final they beat Lanus by the same score to set up the final with River Plate on 13 December 2019, losing 3–0 in Mendoza.