George Gardner, portrayed by Timothy Bottoms, shares a heartfelt bond with his 12-year-old son, David (played by Hunter Carson), as they marvel at the stars and dream of cosmic adventures. One fateful night, a fierce thunderstorm awakens David, who becomes awestruck by a mysterious alien spacecraft that lands on Copper Hill, right outside their home. George, compelled by curiosity, goes to investigate, but when he returns, he is not the same man.
As dawn breaks, David is distressed to find his father wearing only one slipper and exhibiting a notably gloomy demeanor, a stark contrast to George's usual jovial self. An unusual wound—shaped like an 'X'—appears on the back of George's neck, raising David's alarm as he witnesses his father's bizarre behavior. Concerned, David rushes to his mother, Helen Gardner (played by Laraine Newman), but her reassurances fall flat when George inexplicably vanishes, prompting Helen to call the authorities.
Local police, led by Chief (Jimmy Hunt), launch an investigation into Copper Hill. Just as they begin, George reappears alongside the officers, who bear strange, altered personalities that only David seems to notice. Amidst the night, David stealthily observes his parents vanishing over the ridge. The following day reveals a startling change in Helen as she serves burnt bacon and salivates over raw hamburger, prompting David to reject her offer of a trip to Copper Hill.
In a twist of fate, David overhears his teacher, [Mrs. McKeltch](Louise Fletcher) discussing an ominous plan with the police chief. Investigating further, David sneaks into her office, only to discover her consuming a live frog. A frantic chase ensues, but Nurse Linda Magnusson intervenes and invites David to share his concerns regarding the unidentified flying object that has taken hold of his family and friends' personalities.
Despite Linda’s guidance, the situation escalates dangerously when Mrs. McKeltch attempts to seize David, leading him into the depths of an alien cave. Here, David encounters an eerie round alien creature that appears to be involved in the rampant mind control plaguing their town. Just as he attempts to flee, he champions his plea for his parents' safety to Linda, who now faces the daunting task of protecting David from the lurking dangers.
Together, they navigate a terrifying landscape of disappearing alien bases and tension-filled military encounters led by General [Wilson](James Karen). As chaos unfolds, David’s determination to rescue his parents solidifies, leading him deeper into the heart of the alien threat. A climactic battle ensues between David, Linda, and the extraterrestrial forces, as David creatively utilizes his copper penny to activate alien technology and turn the tide.
Just when it seems all hope is lost and his parents are lost to him, David experiences an abrupt awakening—only to find himself safely in his bedroom. His parents comfort him, dispelling the fear that the alien invasion was anything more than a fleeting nightmare. However, tranquility is short-lived as a thunderstorm jolts him awake once again, and he gazes out the window to see the very same UFO descend upon Copper Hill—leaving him questioning the fine line between dreams and reality as his nightmarish adventure threatens to commence once more.