Two drifters, Joe Gruen and Art Burns, find themselves at loose ends on a Saturday night in a small town. They split up and Joe, who has been drinking, drives off in their car to look for girls while Art returns to their room. While driving around, Joe sees a spaceship land and heads toward the landing site. Back in town, Joan Hayden, daughter of the city attorney, and her boyfriend, Johnny Carter, are planning to elope that night, but first head to Lovers’ Point, a popular spot for romance located on farmer Larkin’s property. Larkin has a continuing feud with the young couples who trespass on his land and feed beer to his favorite bull. When Joe returns to tell Art about his find, Art assumes that his friend has had too much to drink. Meanwhile, Lt. Wilkins, a military public relations officer, has been informed of the spaceship’s landing and alerts his superior, Col. Ambrose. As they leave Lovers’ Point, Johnny and Joan almost collide with a jeep carrying Wilkins, the colonel and two soldiers, and later run over what they think is a young boy, but discover is an alien from the spaceship. After a gnarly hand detaches itself from the dead creature and punctures one of the tires on Johnny’s car with needle-like instruments it can extend and retract from its fingers, Johnny and Joan decide to risk going to Larkin’s farmhouse to phone for help. Meanwhile, Wilkins and the colonel reach the spaceship and radio for engineering help to enter it. Larkin is not home when Johnny and Joan arrive to phone the police, who regard their report of running over an alien as a teenage prank. As Joe drives back to the ship, he sees Johnny’s car with the alien’s body lodged underneath the front wheels. After Larkin returns home and orders Johnny and Joan off his property at shotgun point, he leaves again. Soon after, Joe arrives, phones Art and tells him to empty their refrigerator, as he intends to store the alien’s body in it. However, when Joe returns to Johnny's car, a creature kills him with a lethal injection. When Johnny and Joan find their car surrounded by several of the creatures, they run to a nearby highway. At the landing site, the military, unable to open the spacecraft by conventional means, use acetylene torches on its hull, causing it to explode and disintegrate. Meanwhile, the police discover Joe’s body and, remembering Johnny's phone call, arrest Johnny and Joan for murder because they had admitted running into something. Although Joan’s father does not believe their story about the aliens, he offers to help his daughter, but refuses to aid Johnny, of whom he does not approve. Johnny and Joan escape from the police station, steal a detective’s patrol car and head back to the scene of the accident to look for clues to prove their story. While they are searching, the severed alien hand crawls into the police car and, as Johnny and Joan drive back to town, the hand attempts to attack Joan. The couple stops the car, gets out and locks the hand inside, hoping that it will provide the hard evidence they need. Remembering that Joan’s father had remarked that probably only Art would be interested in the details of his friend’s death, they decide to bring Art to see the hand. After they locate Art, he agrees to accompany them in Joan’s car. Meanwhile, one creature has incapacitated Larkin’s bull while others attempt to free the hand. When Johnny, Joan and Art arrive, they shine a spotlight into Johnny’s car and Art sees the hand. Before Art can photograph it, however, the hand evaporates in front of them. The creatures then surround the trio and although Art shoots a gun at them to no effect, the aliens are partially disabled by the car's headlights until the battery dies. Joan and Johnny manage to escape, but Art is captured. Joan persuades Johnny that they should surrender to the police but, when they phone the station from Larkin’s house, they learn that the charges against them have been dropped because an autopsy has determined that Joe died of heart failure due to his blood's extremely high alcohol content. When the police refuse to help them, Joan suggests that they seek help from the couples at Lovers' Point. After several couples circle their cars around the aliens and turn on their headlights, the panicked aliens emit smoke, then explode. When Johnny discovers a very drunk Art, he realizes that the aliens have been injecting pure alcohol into their victims to disable or kill them. After Larkin finds his drunken bull, he suspects the teenagers of inebriating the animal and orders them off his property. Joan and Johnny then resume their elopement.