At a zoo, a cage was reserved for Taz. He soon escapes and runs amok, resulting everyone in the zoo (including the zookeeper) to run away in fear. Meanwhile, Daffy is at home in his duck pond, and reads about Taz's escape in a newspaper. Taz soon finds him and gives chase after the black mallard. While fleeing from Taz's hungry jaws, Daffy hears a news bulletin posting a $5,000 reward for the Tasmanian Devil's return which also says Taz becomes docile when exposed to music. Using different kinds of music (some of which fail miserably) Daffy eventually resorts to using his own voice to calm the devil. Eventually, after serenading him for ten miles, Daffy leads Taz to his cage, slamming the door on the beast just as his voice was about to give out. After Taz grabs a bill which slipped on the ground, Daffy rushes inside the cage screaming his famous line "it's mine, mine all mine", and beats him up, and reassures the audience that he may be a coward, "but I'm a greeeedy little coward."
Zookeper Burton is likely a reference to John W. Burton, who would later take over as the producer of Warner Bros. Cartoons following Eddie Selzer's retirement in 1958.
The sequence where the customers running away from the zoo in fear at the beginning of the cartoon is reused animation from "Wild Over You".
"Ducking the Devil" is notable for being the only pairing of Daffy Duck and Taz in the Golden Age, and the only Taz cartoon in the Golden Age without Bugs Bunny in it.
Despite that Zookeeper Burton says that Taz becomes docile when exposed to music, Taz seems to not be affected by music that sounds unpleasant to his ears. In this case, Taz didn't like the sound of Scottish pipe music, so when Daffy played music with the Scottish pipe, Taz snatched it away from him and smashed it.