The town goes to the Springfield Botanical Gardens to see the blooming of a Sumatran Century Flower. Because the huge crowd is exactly one person over the maximum legal capacity, Chief Wiggum decides to eject the already unpopular and bitter Moe from the ceremony. However, this otherwise unwelcoming gesture is a blessing in disguise, as when the flower opens, it emits a horrible smell, sickening the townspeople and causing them to flee. When the townspeople starts to drive away from the Botanical Gardens, the Simpsons become trapped in a traffic jam. Homer is informed by Lisa that the traffic is moving, however he accelerates too hard and hits the brakes suddenly. The force sends Maggie flying through the sunroof after her safety belt breaks. Moe, who is incidentally standing depressed on the edge of a bridge about to jump and commit suicide, accidentally catches Maggie just as she is about to fall into the river below the bridge. Moe is then instantly declared a hero, much to his surprise.
The Simpsons let Moe babysit Maggie all the time and she is instantly attached to him. 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 is 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. 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". Marge and Homer later learn that Moe has installed his own baby-monitoring system in Maggie's room and they decide that they have had enough, and as a result, they bar Moe from their house for good.
Moe reverts to being depressed, to the point of him 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, Fat Tony 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 Simpsons' 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 Castellanetas 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 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 apologizes for their injustice against Moe 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.