Needing a draw to ensure their return to the top flight, the Billy Goats raced to a 3-0 halftime lead as they wrapped up the title with two matches to spare.
Cordoba took advantage of slack marking to give Cologne an eighth-minute lead before Daniel Steininger headed into his own net from a corner and Cordoba turned in Dominick Drexler's pass four minutes before halftime.
The Colombian completed his hat-trick with a header in the 65th minute as Cologne won promotion from the second tier for the sixth time since 1999/2000, and the fourth time as champions.
(Writing by Brian Homewood, editing by Pritha Sarkar)
