The film begins with a pair of floating disembodied lips welcoming the audience to a science fiction double feature ("Science Fiction/Double Feature"). Throughout the film, a criminologist from an unspecified point in the future narrates and provides commentary on the events.
In November 1974, following the wedding of their friends, a naïve young couple, Brad Majors and Janet Weiss, get engaged and decide to celebrate with their high school science teacher Dr. Scott, who taught the class where they first met ("Dammit Janet"). En route to Scott's house on a dark and rainy night, they get lost with a flat tire. Seeking a telephone to call for help, the couple walks to a nearby castle ("Over at the Frankenstein Place") where a party is being held. They are accepted in by the strangely dressed inhabitants, led by the butler Riff Raff, the maid Magenta, and a groupie named Columbia, who dance to "The Time Warp". Dr. Frank-N-Furter, a transvestite mad scientist, introduces himself and invites them to stay for the night ("Sweet Transvestite").
With the help of Riff Raff, Frank brings to life a tall, muscular, handsome blond man named Rocky ("The Sword of Damocles"). As Frank vows he can improve Rocky into an ideal man in a week ("I Can Make You a Man"), a head-bandaged motorcyclist named Eddie breaks out of a deep freeze ("Hot Patootie – Bless My Soul"). Frank kills Eddie with an ice axe, justifying it as a "mercy killing". Rocky and Frank depart for the bridal suite. ("I Can Make You a Man (Reprise)")
Brad and Janet are shown to separate bedrooms, where each is visited and seduced by Frank. Meanwhile, Riff Raff and Magenta torment Rocky, who flees the suite. Janet, having learned of Brad's dalliance with Frank, discovers Rocky cowering in his birth tank. While tending to his wounds, Janet seduces Rocky as Magenta and Columbia watch from their bedroom monitor ("Touch-a, Touch-a, Touch-a, Touch Me").
Dr. Scott, now a government investigator of UFOs, comes to the castle in search of his nephew Eddie, who sent him a letter implying part of his brain was removed by aliens. Everyone discovers Janet and Rocky together, enraging Frank. Magenta summons everyone to an uncomfortable dinner, which they soon realize has been prepared from Eddie's mutilated remains ("Eddie"). In the chaos, Janet runs screaming into Rocky's arms, provoking a jealous Frank to chase her through the halls to the lab, where he uses his Medusa Transducer to turn Dr. Scott, Brad, Janet, Rocky, and Columbia into nude statues ("Planet Schmanet Janet/Wise Up Janet Weiss"/"Planet Hotdog").
After dressing the statues in cabaret costumes, Frank "unfreezes" them and leads them in a live cabaret floor show, complete with an RKO tower and a swimming pool ("Rose Tint My World"/"Don't Dream It, Be It"/"Wild and Untamed Thing"). Riff Raff and Magenta interrupt, and announce that due to Frank's extravagance, they are declaring mutiny and returning to their home planet of Transsexual, Transylvania. Frank makes a desperate final plea ("I'm Going Home") but is ignored as Riff Raff kills both him and Columbia with a laser. An enraged Rocky climbs the tower with Frank's body, and, after several shots from the laser, plunges to his death. The castle lifts off into space; Brad, Janet, and Dr. Scott are left crawling in the smog and dirt as the criminologist concludes that the human race is equivalent to insects crawling on the planet's surface: "lost in time, and lost in space... and meaning" ("Super Heroes").
