It is 11 o’clock at night at a lighthouse on a small island, and the clock's pendulum is intermittently deflecting the light from the beacon into a mousehole downstairs, keeping the resident mouse wide awake. The baggy-eyed rodent crawls out of bed, climbs the steps to the beacon, and yanks the plug out of the outlet to turn it off. Polly the parrot immediately flies into the lightkeeper’s bedroom squawking “Lights out! Lights out!” The lightkeeper wakes up shouting, “Grrrreat Scott! It’s that crrrrazy moose (mouse) again!” Consequently, a cargo carrier named Australia crashes into the rocks on the shore of the island, causing several wooden crates to spill overboard. The frustrated captain admonishes the lightkeeper to keep the beacon lit, and the lightkeeper and Polly apologize for the mishap. Hippety Hopper, a baby kangaroo intended for delivery to a city zoo, is inside one of the fallen crates, and after the ship departs, he hops off within the crate until it breaks apart against the rocks, setting him free.
While all this is going on, Sylvester is downstairs sleeping. The lightkeeper abruptly wakes him up, rebuking, “While you sleep, that crrrrazy moose is loose in the hoose!” (which Polly repeats), then orders him to go upstairs to catch him and to "Hurrrry up, now, hurrrry up, now" (which Polly also echoes). Sylvester tells Polly he can catch the mouse in a matter of seconds, and Polly starts counting the seconds.
Hippety then hops into the lighthouse and follows Sylvester up the stairs. Sylvester sets a mousetrap and attaches a string. When he hears a snap, he pulls on the string and sees he has caught Hippety, whom he thinks is a giant mouse, which makes his jaw drop to the floor. Sylvester then shoots like a bullet down the stairs as Polly keeps counting (“542...543...”), and dashes to the bathroom, thinking he must have “lighthouse eyes” or “stigmatism”. He puts in eyedrops, then, grabbing a bottle of vitamins, gulps them down and showers himself with them.
Meanwhile, the mouse frees Hippety from the trap, and Hippety returns the favor by pulling the plug out of the wall. (“Lights out! Lights out!”) Sylvester runs out of the bathroom, tells Polly “Keep counting, buster” (“3,685...3,686...”), runs upstairs, puts the plug back in and pounds a few nails over it to prevent Hippety and the mouse from pulling it out again. He then prepares to knock Hippety out with a club and swings at him when he sees Hippety’s shadow approaching, but misses and sees that it is only the mouse wielding a mallet, which he uses to slam Sylvester’s foot. The mouse then zips behind the elevator door. Sylvester pounds on the door, and Hippety kicks him into the wall. Sylvester then sees Hippety and the mouse behind the door playing a back-and-forth switcheroo, making him think he must be hallucinating. Sylvester then charges back toward the elevator and Sylvester, Hippety and the mouse get into a scuffle, which ends with Hippety sending Sylvester tumbling down the stairs. By this time, Polly has counted more than 70,000 seconds (which in reality is most of a day), but the punch-drunk feline goes back for more, assuring Polly he will get the mouse “quicker than you can count up to Jack Robinson”.
The mouse cuts the extension cord in two places with a pair of scissors, putting the lights out again, and the furious lightkeeper stalks Sylvester with a club threatening to “fix that good-fer-nothin’ pussycat”. In a panic, Sylvester attempts to reconnect the cord and gets a massive electric jolt, which turns the lights back on ("Lights on! Lights on!") and spares him a beating...for the moment.
As Sylvester tapes the cord back together, the mouse rigs dynamite with the cord wrapped around it. It explodes, completely destroying the cord beyond any chance of repair. Immediately, the lightkeeper runs up the stairs and pummels Sylvester with the club.
In the final scene, the lightkeeper is sleeping soundly, as are Hippety and the mouse, while Sylvester is serving as the beacon, hooked up to a battery with the light projecting through his eyes. To this, he laments, “I never thought just being a pussycat could be so complicated!”
On CBS and ABC , the part where Sylvester catches the mouse in an elevator and the elevator door opens and closes, alternately showing Sylvester beating up the mouse and Hippety Hopper (the baby kangaroo that Sylvester mistakes for a giant mouse in the Robert McKimson cartoons) beating up Sylvester was cut (even though it was shown as a teaser clip on CBS's "The Bugs Bunny/Road Runner Show" and ABC's "The Bugs Bunny and Tweety Show")
On Nickelodeon , the part where the mouse uses a pair of household scissors to cut the electric wire was replaced with a repeat shot of Polly squawking, "Lights out! Lights out!"
On the (now-defunct) WB! network , two different scenes were cut:
The scene where Sylvester runs into the bathroom and ingests pills to fix his supposedly faulty eyesight (this scene was left intact on ABC, despite that a similar scene in "The Last Hungry Cat" was cut).
The scene where Sylvester grabs the severed wires and gets electrocuted.