Richard Sturges, Clifton Webb, a wealthy expatriate in Europe, buys a third-class ticket for the maiden voyage of the Titanic from a Basque emigrant. Once aboard, he seeks his runaway wife Julia Barbara Stanwyck and discovers that she is trying to take their two unsuspecting children, 18-year-old Annette Audrey Dalton and 10-year-old Norman Harper Carter, to her hometown of Mackinac Island, Michigan, to rear them as ordinary Americans rather than as privileged elitists in Europe. The passengers also include the wealthy Maude Young Thelma Ritter (based on real-life Titanic survivor Margaret Brown), social-climbing Earl Meeker Allyn Joslyn, 20-year-old Purdue University tennis player Giff Rogers Robert Wagner and George Healey, a Catholic priest who has been defrocked for alcoholism.
As the ship is prepared for departure, Sanderson, the company representative (based on J. Bruce Ismay), suggests to Captain Edward J. Smith Brian Aherne that a record-setting speedy passage would be welcomed. One night on the bridge, Smith asks Second Officer Charles Lightoller about a note from First Officer Murdoch about binoculars, and Lightoller explains that the ship has very few, just enough for the bridge, but none for the lookouts.
When Annette learns of Julia's intentions, she insists on returning to Europe with Richard on the next ship as soon as they reach America. Julia concedes that Annette is old enough to make her own decisions, but she insists on keeping custody of Norman. This angers Richard, forcing her to reveal that Norman is not his son, but rather the result of a brief dalliance after a bitter argument. Richard declares he makes no claim to Norman and does not want to see him again.
Richard joins Maude, Earl and George Widener in the lounge to play auction bridge. The next morning, when Norman reminds him of a shuffleboard game that they had arranged, he coldly rebuffs him. Meanwhile, Giff falls for Annette at first glance. At first, she repulses his brash advances, but she eventually warms to him. That night, Giff, Annette and a group of young people sing and play the piano in the dining room, while Captain Smith watches from a corner table.
Lightoller expresses his concern to Captain Smith about the ship's speed when they receive two messages from other ships warning of iceberg sightings near their route. However, Smith assures him that there is no danger, as the sea is clear and the track is south of the reported icefield.
That night, the lookouts spot an iceberg dead ahead. The crew tries to steer clear of it, but it gashes the side of the bow below the waterline and water breaches the hull. When Richard finds Captain Smith, he insists on the truth, and Smith informs him that the ship is doomed and that there are not enough lifeboats to save everyone on board. Richard tells his family to dress warmly but properly, and they head outside.
Richard and Julia have a tearful reconciliation on the boat deck and he places her, along with Annette and Norman, into a lifeboat. Unnoticed by Julia, Norman volunteers to surrender his seat to an old woman and boards the ship to find Richard. When one of the lines becomes tangled, preventing the boat from being lowered, Giff climbs down and fixes it, only to lose his grip and fall into the water. Meeker disguises himself as a woman to board a lifeboat, but Maude notices his shoes and unmasks him in front of the others. George Healey selflessly heads into grave danger in a boiler room to comfort injured crewmen.
As the Titanic is in her final moments, Norman finds Richard, who tells Norman that he has been proud of him every day of his life. They join the rest of the doomed passengers and crew in singing the hymn
> Nearer, My God, to Thee
As dawn approaches, the survivors are seen in the lifeboats, rowing aimlessly.
