The Simpsons take a trip to the Springfield Botanical Gardens, where a Venus flytrap lures Homer into its mouth using a hotdog for bait. Homer escapes from the plant’s maw by eating his way out. Meanwhile Moe begins to wonder where all his regular barflies have gone. He looks up at the television and sees Kent Brockman filing a news report from the gardens. Brockman reports that people have gathered to watch the blossoming of the Sumatran Century Flower, which happens once every hundred years. Moe decides to close the bar and join everyone else. When he arrives, Wiggum announces that gardens have filled to maximum capacity and someone must leave. He notices Moe and rolls him down a muddy hill. A short time later, the plant blossoms, releasing a noxious odor into the air. People start to run for the exits, and soon after a huge traffic jam forms on the highway. With traffic at a standstill Carl, Lenny, and others gather at Dr. Hibbert’s mini-van, which is equipped with a television set. When the traffic moves Homer hits the accelerator, but when he reaches the crest of a bridge the traffic jam resumes. He hits the brakes, causing Maggie to fly out of her car seat and into the air. As the baby drops Homer runs to the bridge, his arms outstretched, but Maggie plummets past him. Below, a despondent Moe stands on the side of the bridge, preparing to jump. He holds out his arms to dive, and Maggie suddenly lands in them. Witnesses proclaim Moe a hero.

Moe stops by the Simpson home to play with the baby, and a close bond soon develops. Meanwhile, Marge chases after Grampa when he suddenly runs down the street naked. When she returns home she discovers Moe and Maggie having a tea party…one that suspiciously resembles Moe’s bar. Marge asks Moe if he’d be willing to baby-sit, and he agrees. Later, when Moe comes over to the house to baby-sit Maggie, he entertains her with the story of The Godfather and sticks an orange in his mouth to tell part of the story. Maggie claps, happily. Soon after, Homer and Marge begin to worry that Moe is closer to Maggie than they are. When the baby starts to cry, Bart phones the bar and asks Moe for help. He then holds the phone to the baby, and Moe soothes her with his voice. When Maggie’s birthday arrives, Moe gives her dollhouse-sized version of his tavern. That night, when the baby begins to cry, Homer finds Moe in her room, calming her. Moe explains that he has a baby monitor in the room. Homer and Marge react with shock, and Homer forbids Moe from seeing the baby.

Moe experiences withdrawal syndrome now that Maggie is no longer part of his life. One day, Fat Tony and his boys meet outside Maggie’s window to discuss an upcoming hit on mobster Don Castellaneta’s family. Fat Tony does a Godfather impression using an orange slice, getting Maggie’s attention. When they walk off, she follows them. Marge discovers the empty baby crib and immediately suspects Moe is to blame. The police break down Moe’s door, but find no sign of the missing child. Later, Marge finds a clue: a discarded orange wedge. Moe asks if mobsters ever plan hits outside the house, and Marge confirms it happens all the time. Moe tells Marge and Homer they must make a trip to Little Italy. Meanwhile, a stand-off occurs inside Luigi’s restaurant when Fat Tony and his boys draw their guns on the Castellaneta family, and the Castellanetas, in turn, draw their guns. Caught in the middle is baby Maggie, who followed Fat Tony into the restaurant. Moe spots the baby in the eatery and bravely walks inside. The mobsters are so touched by his story about befriending the baby that they let him leave. Marge thanks Moe for saving the baby’s life yet again. Homer tells everyone he has an idea for letting Moe and Maggie spend more time together. Later, Homer takes Maggie to the bar, where Moe changes the channel on the television, switching from a baseball game to “The Happy Little Elves.”