The goal came somewhat out of the blue as Behan, who had scored in Cork's 2-0 win over Drogheda earlier in the competition, let fly from 25 yards.
The shot seemed to deceive keeper Dan Connor and went in off the far post.
Connor was shown a straight red card on 83 minutes for a push on Behan and now misses Droheda's semi-final. George O'Callaghan slotted home the resultant penalty.