Andrea Paolucci gave the visitors the lead in the 41st minute with an excellent free-kick and the upset appeared to be on.
However, early in the second half Massimiliano Busellato received two yellow cards in successive minutes to reduce Cittadella to 10 and they were left with only nine men when Edoardo Gorini also joined him for an early bath in the 68th minute.
Nevertheless, it was not until the 88th minute that Argentine Gonzalo Bergessio managed to equalise and the in the sixth minute of stoppage time Francesco Lodi curled in a free-kick that the goalkeeper should have saved.
Catania's reward for their win will be a last 16 tie against Parma.
