A five-goal away win in the first leg gave Odense a good chance to reach the quarter-finals, but Odense did not get off to a great start, and after six minutes in Denmark, the home team's position looked shaky.
Alicia Toublanc and Kristin Thorleifsdottir looked in blistering form, allowing Debrecen to pull in front (6-2), forcing Odense's coach Jakob Verstergaard, to take an early timeout.
However, the timeout did not have the desired effect for Odense, as the visitors continued to dominate and were leading by five goals (15-10) two minutes before the break.
But then Odense finally found their rhythm and started to catch up, drawing level in the 40th minute at 22-22.
Debrecen converted just two of their seven penalty shots, as Odense's goalkeeper Yara ten Holte finished the game with 14 saves.
In the last 20 minutes, the game was very balanced, and the home team felt comfortable, ultimately snatching a draw after Andrea Aagot Hansen's goal with 22 seconds to go and Océane Sercien-Ugolin's last-second penalty miss.