Elmer is ready for bedtime, but Sylvester has other plans as he starts singing in Elmer's back yard. A series of gags play out, as Elmer tries everything up his sleeve to get rid of that unwanted pest. Elmer eventually confronts Sylvester, but before Elmer can blast him with his shotgun, Sylvester sings a sweet, gentle lullaby to ease him to dreams. However, this doesn't last, and the insanity continues…
Elmer eventually dies from explosives from his attempts to get rid of Sylvester. He winds up in Heaven, as an angel on a cloud. Momentarily he thinks he will finally get some peace and quiet. However, the spirits of Sylvester's nine lives continue to sing as they ascend around him, each with a numeral on her back (there are actually more like 18 Sylvesters depicted overall), singing the sextet from "Lucia di Lammermoor". The exasperated Elmer dives off his cloud and a crash is heard off-screen.
The cartoon is a remake of 1941's Notes to You, also directed by Freleng. It has a similar plot (although the ending of the original doesn't have the characters die from an explosion; instead the cat dies from getting shot, and returns as nine singing angels), but the Elmer and Sylvester characters in Notes to You were taken by Porky Pig and an unnamed alley cat (the latter bearing a striking resemblance to the cat from Bob Clampett's The Hep Cat).
Back Alley Oproar is notable in the Warner cartoon canon as one of the very few shorts in which Sylvester actually "wins out" over another character, albeit at the presumed cost of his life.