Johnny Dalton, Frank Sinatra, a teller at the Meek California Fidelity Trust, asks his boss J. L. McKissack, Harry Hayden, for a raise so he can marry Mildred "Mibs" Goodhue, Jane Russell. Emile J. Keck, Groucho Marx, a friend and waiter at the Italian restaurant they frequent, also urges Johnny to take a chance, facetiously suggesting the idea of robbing the bank. When Johnny chooses to wait, Mibs storms out, setting the stage for a complicated chain of events that blends naivety, luck, and deception.
On the way back to work, Johnny intervenes when he sees two men beating up a third in an alley. The victim, "Hot Horse" Harris, the Bookie Nestor Paiva, expresses his gratitude by handing Johnny $1,000. Johnny initially declines, but Harris converts the gesture into a “loan,” then bets the entire amount on a sure thing in a fixed race, making sure to place the bet at the bookie joint run by his competitor. The win turns into a windfall: from the winnings, Harris takes back the loan, leaving Johnny with $5,000, and then Harris places two more bets for Johnny, both winners. Johnny's total climbs to $60,000, while Harris only holds $40,000 on hand and promises to send the rest later. Johnny rushes to share the news with Emile, but Emile reads it as a sign of bank robbery rather than good luck.
The celebration is short-lived: the bank's auditors have discovered that $75,000 is missing. Fearing it will look like a crime, Johnny enlists Emile’s help to hide the money, while he also tries to tell Mibs about his windfall—though she remains skeptical at first. Mibs eventually finds $20,000, the remainder of what Harris owes Johnny, and goes to see Bob Pulsifer Jr., Don McGuire, the lazy, lecherous son of the bank's founder. She offers the money on condition that he stay silent, but he phones the police anyway. Emile poses as a millionaire and redeposits the funds in Johnny's bank, a tactic meant to draw police attention away from the real source of the money. This move catches the eye of R. B. Pulsifer Sr., the reclusive head of the Board of Directors, Howard Freeman, who invites Emile to check into an exclusive hotel under the millionaires’ ruse.
Emile’s performance and the growing friendship with Pulsifer Sr. help to clear Johnny in the end, even as Mibs and Johnny are briefly pursued toward Mexico. The couple is caught, but not for the windfall itself; instead, the auditors track the $75,000 to Mibs. Johnny discovers—almost by accident—that Mibs’s adding machine is malfunctioning: 2+2 = 5 and 3+3 = 7. Afterward, Mibs confides in a man she thinks is a reporter about Johnny’s gifts, only to learn that the man actually works for the IRS. The fallout reshapes the relationships around them: McKissack, who had been fired for falsely accusing Johnny and Mildred, ends up taking Emile’s old waiter job, while the real resolution centers on clearing Johnny and stabilizing his future with Mibs.
