Genteel intrigue unfolds as Philo Vance, a discerning gentleman detective, begins an intricate case after receiving an anonymous letter warning that Lynn Llewellyn will be in danger when he appears at the casino owned by his uncle, Kinkaid. Vance visits the Llewellyn estate, run by Mrs. Llewellyn, the family matriarch, and immediately steps into a heated family quarrel that exposes fragile loyalties and simmering resentments within the clan. The dispute centers on Virginia, Lynn's wife, who announces she intends to leave the house for Chicago, sending shockwaves through the mansion. During the discord, Vance and Doris, Mrs. Llewellyn's secretary, meet and quickly sense a growing mutual interest that adds a personal tension to the investigation.
Vance takes Doris to his home, where he and District Attorney Markham examine the mysterious letter. Doris quickly identifies a crucial clue: the return address points to the Llewellyn townhouse in Closter, and the letter was typed on her own typewriter. To help monitor the casino that night, Sergeant Heath is assigned, but the evening ends with Lynn collapsing at the card table, launching a trail of puzzling events and sudden danger. Virginia’s death shortly afterward compounds the mystery and intensifies the urgency of solving the case before further harm occurs.
Back at the estate, investigators press the family circle. Amelia, Mrs. Llewellyn's daughter, admits she also had a spat with Virginia, while Mrs. Llewellyn recounts a prior quarrel with her daughter-in-law. Doris uncovers Mrs. Llewellyn's recently altered will, which disinherits Kinkaid and leaves Lynn and Amelia as the primary beneficiaries of the estate. Additional clues surface, including Kinkaid's unusual collection of books on chemistry and poisons and a loaded gun found in Virginia's bedroom, painting a picture of potential danger lurking in the household.
After Lynn recovers, Mrs. Llewellyn is found dead with a note signed in her hand, confessing to Virginia's murder, a twist that tests Vance's confidence in his deductions. He pursues his theory and discovers a secret laboratory where Kinkaid has been producing heavy water, a finding that hints at a more elaborate, potentially dangerous scheme. Kinkaid is captured and briefly held, but Vance remains unconvinced that he is the killer, seeing him as a decoy within a larger intrigue that could involve others.
The true killer is eventually revealed: Lynn, who had dosed himself with a small amount of poison to stage his “perfect crime” and lure Vance and Doris to the Closter townhouse. Before Lynn completes his plan, Vance reads from a letter he previously penned that lays out his full theory, naming Lynn as the murderer—a rich, egomaniacal weakling who poisoned his wife and framed his uncle. Lynn attempts to deflect blame onto Kinkaid, but the evidence and Vance’s careful reasoning leave little room for doubt. When Lynn shoots at Vance, Sergeant Heath and others spring from behind a door, arresting the killer in a decisive moment. In the aftermath, Becky, Mrs. Llewellyn's maid, is thanked for loading Lynn's gun with blanks, and [Doris] remains by Vance's side as they resume their budding romance, wiser and ready to face whatever mystery may come next.