At a deserted New York nightclub, gangster Johnny Yonkers murders a man named Battaglia, who is playing the tune "One for My Baby" on the piano. Seconds later, a woman enters and, realizing what has happened, flees just as Johnny fires two shots at her. Johnny is charged with Battaglia's murder but plans to plead self-defense. Aware that the district attorney is looking for the eyewitness, Johnny arranges for a hired killer to find the woman, whose identity he has deduced. Soon after, a man named Matt Hallett arrives at Montana's Glacier National Park and checks in at the large resort hotel. There, Matt meets Mary Tiller, a young Blackfoot woman who works in the gift shop; suspicious ranger Joe Parker; and Paul Adams, a commercial photographer on assignment. Matt also meets cashier Louise Graham, and after she rebuffs his flirtations, sends a telegram to New York stating that "our friend is here." That evening, Matt escorts Mary to a dance at a luxurious house built into the side of a mountain. As Paul, who came with Louise, dances with Mary, Parker shows Matt a wanted poster for Mary's father Katoonai, who is being sought on murder charges. Later, Matt asks Louise to dance, but when the song "One for My Baby" is played on the jukebox, she becomes agitated. Soon after, an avalanche sends rocks cascading into the house, causing the power lines to explode. Parker is impressed when Matt scales the electrical pole outside the house and disables the power. The next day, during a Blackfoot ceremonial dance, Matt invites Louise to go walking and asks her about her relationship with Paul and why she was upset by the song. While standing on the edge of a cliff, Louise recalls strains of the tune and screams. Matt grabs Louise just as Paul comes looking for her. Later that afternoon, Mary receives an award at the elementary school she once attended, but when she sees her father peering proudly from a trap door in the ceiling, she faints. That evening, at the hotel bar, Elster, an emissary from Johnny posing as a jovial guest, approaches Paul and warns him that the gangster is impatiently waiting for him to eliminate Louise. Nervously, Paul seeks out Louise and asks her to go for a ride, but before they can leave, Parker commandeers him and Matt to help fight a forest fire. As they battle the fire, Matt and Paul are trapped in the flames and Matt saves Paul's life. Upon returning to the lodge, Paul, who is involved in a clandestine affair with Mary, uses his concern for the girl as a pretense to talk to Louise alone. Matt is called to the phone before he can stop Louise from driving away in Paul's car, and after he hangs up, he informs Parker that he is a New York detective and asks the ranger's help in arresting Paul. As Paul and Louise drive along a mountain road, a bulletin from ranger headquarters comes over their car radio, warning that Paul is a dangerous gunman dispatched to kill Louise. Screaming in fear, Louise jumps out of the car and Paul swerves around, trying to run her over. Pushed over the roadside embankment, Louise lands safely in the brush and pulls herself back onto the road, where she is picked up by a motorist and taken to the ranger station. Paul, meanwhile, speeds to Mary's room and informs her that the rangers want to arrest him. Claiming that his car was stolen and used in a robbery, Paul enlists Mary's help in fleeing the park. Matt, meanwhile, takes Louise for a boat ride on a lake and, after confessing that he has fallen in love with her, presses her to testify against Johnny. Upon reaching the lodge, they find a note from Mary, and when a fisherman directs them to Paul's abandoned car, Louise leads Matt to an Indian cave in which she thinks Paul may be hiding. Near the cave, they encounter Katoonai, who fears that Mary and Paul will cut across a dangerous glacier to exit the park. As Mary and Paul approach the glacier, Katoonai sees them and instructs Matt to pin down Paul with gunfire while he climbs onto the ledge above. Paul spots Katoonai, however, and shoots him from his perch, sending him careening to his death. Horrified, Mary struggles with Paul, who throws her against the rocks and takes her hostage, forcing her to continue. Matt and Louise follow, and Mary grapples with Paul again, sending his gun flying into the snow. Matt then jumps Paul, and as the two men fight, Louise reaches for the discarded gun. The added weight causes the snow to crumble, and Louise plummets to an ice shelf below. After throwing Paul onto another ice shelf, Matt, with Mary's help, lowers himself by rope to rescue Louise. Regaining his balance, Paul grabs for the gun and fires at Matt. The noise of the gunshots triggers the collapse of the glacier, causing it to topple over and crush Paul. After tying the rope around Louise's waist, Matt pulls her to safety. Drawn by the sound of gunfire, the rangers then appear, and in relief, Matt and Louise kiss and plan a happy future together.