Tina Gray (Amanda Wyss) has a dream in which she is stalked through a dark boiler room by a mutilated figure with distinctive razor-sharp knives attached to the fingers on his right hand. Just as he catches her, however, she wakes up screaming, only to discover four razor cuts in her nightdress identical to the cuts in her dream.
The next day, she finds out that her friend Nancy Thompson (Heather Langenkamp) experienced a similar dream involving the same sinister figure, but Nancy is convinced that all is well. That night, Tina, Nancy and her boyfriend Glen Lantz (Johnny Depp) have a sleep-over to make the distraught Tina feel better, as she is still troubled by her nightmare. Tina's rebellious boyfriend, Rod Lane (Nick Corri), crashes the party. He and Tina have sex in her mother's bedroom. However, Tina has another nightmare, and this time the killer catches and murders her brutally. Rod wakes up to find Tina being cut open by invisible knives, then dragged up the wall and across the ceiling. Rod, being the only other person in the room at the time, is accused of the murder, flees the house and is caught the next day.
Nancy then has three violent nightmares in which she is viciously stalked, then attacked, by the same terrifying figure who attacked Tina. These nightmares cause her to talk to Rod in jail, who tells her what he saw in Tina's mother's bedroom, and also remarks he had a nightmare involving the fiend with the "knives for fingers". Much to the dismay of her mother Marge (Ronee Blakley), Nancy becomes increasingly convinced that the figure appearing in her dreams is the person who killed Tina. Nancy and a skeptical Glen rush to the police station late at night to talk to Rod, only to find that he's been strangled by his own bedsheets. To everyone except Nancy, it appears to be a suicide.
Nancy's mother takes her to a Dream Therapy Clinic to ensure she gets some sleep. Once again, she has a horrendous nightmare. This time, her arm is badly cut, but she finds that she has brought something out from her dream: the killer's battered hat. It arouses concern, but also other feelings in Marge, who is clearly hiding a secret. Eventually, while drunk, Marge reveals to Nancy that the owner of the hat, and the killer, was a man named Fred Krueger (Robert Englund), a child murderer who killed at least twenty children over a decade earlier. Furious, vengeful parents burned him alive in his boiler room hideout when he was released from prison on a technicality due to an improperly signed search warrant. Now, it appears he is manipulating the dreams of their children to exact his revenge from beyond the grave. Nancy's mother, however, reassures Nancy that Krueger cannot hurt anyone, pulling Krueger's bladed glove from a hiding place in the furnace as proof. Eventually, Marge installs bars on all the windows and begins to lock the door as "security".
Nancy and Glen devise a plan to catch Krueger, but when Glen falls asleep that night he is pulled into his bed and regurgitated as a spew of gore and bone. Nancy is left alone with Krueger after pulling him out of her dream into the real world. She runs around her house and forces him to run into booby traps she had set earlier. After setting Krueger on fire Nancy locks him in the basement and finally gets her father, police lieutenant Donald Thompson (John Saxon) and the rest of the police to help. After discovering that Krueger has escaped and that fiery footsteps lead upstairs, Nancy and her father witness Krueger smothering Marge with his flaming body, disappearing to leave her corpse to sink into the bed. After sending her father away, Nancy faces Krueger on her own and succeeds in destroying him by turning her back on him and draining him of all energy.
The scene changes to the next morning as Nancy gets in a car with Glen and the rest of her friends, on their way to school. Krueger possesses the car just as she gets in. The car drives away with Nancy screaming for her mother, and Marge being pulled through the door window by Krueger's bladed hand.