Lisa leads the Simpsons to the Springfield Botanical Gardens, where the Sumatran Century Flower is about to bloom for the first time in 100 years. Moe, wondering where his regular customers are, discovers that most of the town has turned out for the botanical event. He closes his bar and proceeds to uncomfortably join the throng. Unfortunately, the crowd size for the event has exceeded the garden's capacity by one person, and Chief Wiggum makes Moe leave. When the plant blooms, it releases a ghastly stench that makes the townspeople flee for their lives, destroying the botanical gardens. Moe walks sadly away from the gardens, mistaking the townspeople’s screams of delight. While attempting to escape the plant's noxious fumes, the crowd causes a terrible traffic jam that bottlenecks at the Springfield Bridge. Thinking the traffic has finally cleared, Homer floors the accelerator but then must suddenly slam on the brakes, causing Maggie's car seat restraints to snap. Maggie goes flying through the car's sunroof. Moe, having decided to end it all, is just about to jump off the bridge when Maggie lands in his arms. The crowd deems Moe a hero, and when Maggie gives her surprised rescuer a kiss, suddenly life does not seem so bad to the surly bartender.
Moe shows up at the Simpson house, and when Homer leaves for work and Marge ends up having to deal with Grampa, Moe is left babysitting Maggie. Maggie is instantly attached to Moe, and they have a good time. Marge returns and Moe asks if he can babysit Maggie, and she agrees. After a while, Marge is happy that she has had plenty of time to get things done, but Homer feels left out of Maggie's life and worries because she's his last chance to be a good father. Later, Moe tells Maggie the story of The Godfather. When he gets to the part where Don Corleone plays with his grandson, Moe demonstrates how the Don scares him by sticking a cut-up orange in his mouth, and Maggie enjoys it. Furthermore, he explains the entire baptism sequence to her, including the ever-popular death scene of Moe Greene, who was shot clean through the eye. Moe uses a teddy bear and points at the bear's eye to portray that Greene was shot in the eye. He later goes on to tell her the sequel. When it comes to Maggie's birthday party, Moe annoys everyone with his behavior and his gift to Maggie: a toy-sized rendition of his bar, featuring "Classic Drunk Barney" and "Drunk Talking Homer" (whose recorded line, "I peed my pants", was taped for Homer's private use). Marge and Homer later learn that Moe has installed his own baby-monitoring system in Maggie's room and they decide that they've had enough.
Moe reverts to being depressed, to the point of Moe imagining the barflies as Maggie. One night, the family is asleep, and Maggie wakes up and hears the mafia outside the house, plotting to kill the Castellaneta family. When one of the mobsters feels hesitant, he does the Godfather-orange routine to cheer him up, and Maggie recognizes it. She decides to follow the mobsters. When Homer and Marge find her missing, they automatically assume that Moe kidnapped her, and they track him down. They see Moe at his oven, and they think that Maggie is inside (it turns out to really be a ham). When Moe is told that Maggie is missing, his request to help find her is granted by Homer. The group decides to search the Simpson's house yard. They find the cut-up orange that was used by Fat Tony, and Moe works out that Maggie must have followed them.
Maggie follows the mobsters to Luigi's, where Fat Tony's gang and the Castallanetas are having a meeting. Maggie enters the restaurant where the two gangs are about to start a gun battle. The situation deteriorates when both groups of mobsters are aiming weapons at each other (with the angry head of the Italian Anti-Defamation League pointing guns at both sides) and Maggie is in the middle of an "Italian-American Mexican standoff". Homer, Marge and Moe are standing outside and Moe decides to go inside and save Maggie. Moe goes inside, and to prevent being shot, tells the gangsters about Maggie's innocence and how it redeemed his life. They start to cry, and Moe and Maggie are safe to leave. The family and Moe make up in the end, and Homer and Moe decide to have a "playdate": Homer spends quality time with the ham, and Moe spends more time with Maggie. It ends with more of "You're My Best Friend" by Queen and a picture montage of Homer with Moe's ham.