Vincent MacKenna (Bill Murray) is telling a joke about an Irish worker to some people at a bar. It's not very funny and no one seems to get it. From there, we learn that he is an alcoholic who lives alone with his cat Felix. He is in a sexual relationship with a pregnant Russian stripper named Daka (Naomi Watts). Vin tries but fails to sell his home with the bank. He then tries to close his account, only to be told that he has overdrawn about $114. At night, he tries to cut a block of ice for his drink with a hammer, only to accidentally smash his hand and then bang his head against the cupboard in frustration, knocking himself out.
The next day, a couple of movers back their truck into the tree in front of Vin's home, while also wrecking his fence. A branch falls off and lands on Vin's car. He wakes up and goes to confront the movers. Vin's new neighbor, Maggie Bronstein (Melissa McCarthy), gets out of her car to defend the movers, as it is she that they are helping move into her new home with her son Oliver (Jaeden Lieberher). Vin is rude to both the movers and Maggie, telling them that one way or another, they'll pay for the damages.
Oliver is shown to be a precocious kid. Maggie enrolls him at the St. Patrick Catholic School. She is unable to take him to school or pick him up as she is floored with work at her job as a CAT scan technician. Oliver has to take the bus to school. He goes to class taught by Brother Geraghty (Chris O'Dowd). He asks Oliver to do the morning prayer, only for the boy to state that he's Jewish. The other kids in the class admit they practice different religions, and one girl outright states there is no God. Oliver is later picked on by a some boys after gym class, and then he has his uniform stolen along with his house keys and phone.
Vin is at the racetrack trying to bet on horses. A man named Zucko (Terrence Howard) approaches him. He and Vin have some shady business together for which Vin owes Zucko money. The horse that Vin bets on also happens to lose.
Oliver asks Vin to use his phone to call his mom. Vin speaks to Maggie and tells her that if he is going to be babysitting Oliver, he is going to charge her $12 an hour. She reluctantly agrees.
Since Maggie is forced to stay working overtime, Oliver continues to spend time with Vin. While he tries to call his mom from a payphone, Oliver is harassed by the bullies from school, led by Robert Ocinski (Dario Barosso). He's mad at Oliver for getting him in detention for stealing his stuff, and he pushes Oliver against the payphone, giving him a bloody nose. Vin comes by and calls Robert out since he knows the boy's mother. Vin threatens the boys and breaks Robert's skateboard, making them run off.
Vin later takes Oliver to a nursing home to visit Vin's wife Sandy (Dorina Mitchell), who suffers from Alzheimer's and hardly recognizes Vin. Vin spends time with her and even does her laundry. Afterwards, Vin takes Oliver back to his house and shows him how to fight.
After work, Maggie is found by a man that serves her a subpoena. Her ex-husband David is seeking custody of Oliver.
At school, the kids are playing dodgeball. Robert throws the ball in Oliver's face. He stands up and calls Robert an "asshole dickbag son of a whore" before running and uppercutting him like Vin showed him.
Vin takes Oliver to the tracks to continue his betting. Oliver gives the names of three horses he is betting on. He throws in $7 while Vin throws in $3. They win their bet, but Vin has to hide his excitement with Zucko watching in the back. With this money, he opens up a savings account by pretending Oliver is his grandson. He later takes Oliver to the bar.
Maggie meets with Geraghty and the school's principal over the fight Oliver had. She tells them that the boy is adopted and that David cheated on her with three different women. All this, coupled with her work, has been extremely stressful for her.
Oliver serves detention with Robert by cleaning the bathroom. They slowly develop a bond and become friendly with each other.
Vin faces a dilemma when the nursing home is trying to move Sandy into another location. Vin also has to score money with Daka's help by trying to sell drugs.
He ends up withdrawing all the money from the savings account. When he gets home, he finds Zucko and his goon waiting for him. Vin attempts to fight the goon, only to fall down as he suffers a stroke. Zucko tells the goon they need to leave now.
Vin is taken to the hospital. He is fine, but his speech and motor skills are temporarily impaired. Maggie, Oliver, and Daka help rehabilitate him and also clean up his home. However, when he returns home, he gets a call from the nursing home and learns that Sandy passed away. He is given her cremated remains in a box. This later causes him to be cold toward Oliver when he tries to console him.
Maggie goes to court to fight David (Scott Adsit) for custody over their son. She then learns of all the things Oliver has done with Vin, like going to the bar, tracks, and being around Daka. The judge grants Maggie and David shared custody of Oliver.
Oliver's class is given an assignment on a modern day saint. He goes around town interviewing people close to Vin, including Daka. The boy learns that Vin served in Vietnam and begins to work on his assignment.
Daka tells Vin that her water broke and makes him drive to the hospital. However, they first make a stop at Oliver's school where he is giving his presentation.
He talks about Vin's work in serving his country and taking care of his ailing wife prior to her passing, as well as how he has taken care of him when his mom wasn't around. Oliver says that while Vin is flawed, he is a saint for all the work he has put in for those around him. He dubs his neighbor "Saint Vincent". The whole auditorium cheers and applauds Vin as he goes to take the stage alongside Oliver. He puts a medal on Vin and gives him a hug.
Daka later gives birth to a healthy baby girl. She and Vin take care of her in his home (it's more or less implied that Vin is the father).
Vin later holds a dinner in his home with Maggie, Oliver, Robert, Daka, and her baby. Oliver suggests Vin says grace, and though it looks like he's gonna start, he decides not to. Daka then starts to breastfeed the baby in front of the boys until Maggie puts a cloth over her.
The credits show Vin sitting outside listening to a song and singing along to it.