Kara Zor-El (Helen Slater) lives in an isolated Kryptonian community called Argo City, in a pocket of trans-dimensional space. Zaltar (Peter O'Toole) allows Kara to see a unique and immensely powerful item known as the Omegahedron, a baseball-sized sphere which he has borrowed without the knowledge of the city government, and which powers the city. However, after a mishap, the Omegahedron is blown out into space. Much to the distress of her parents (Simon Ward and Mia Farrow), Kara follows it to Earth (undergoing a transformation into "Supergirl" in the process) in an effort to recover it and save the city.On Earth, the Omegahedron is recovered by Selena (Faye Dunaway), a power-hungry would-be black magic witch assisted by the feckless and long-suffering Bianca (Brenda Vaccaro) and seeking to free herself from her relationship with warlock Nigel (Peter Cook). Whilst not knowing exactly what it is, Selena quickly realizes that the Omegahedron is powerful and can enable her to perform real magical spells. Supergirl arrives on Earth and discovers her powers. Following the path of the Omegahedron, she takes the name Linda Lee, identifies herself as a cousin of Clark Kent (whom as Superman is off worlds), and enrolls at an all-girls school where she befriends Lucy Lane (Maureen Teefy), the younger sister of Lois Lane who happens to be studying there. Kara also meets and becomes enamoured with Ethan (Hart Bochner) who works as a groundskeeper at the school.Ethan also catches the eye of Selena, who drugs him with a potion to make him love her. However, Ethan regains consciousness in Selena's absence and wanders out into the streets. An angry Selena uses her new-found powers to animate a construction vehicle, which she sends to bring Ethan back, causing chaos in the streets as it does so. Kara rescues Ethan and he falls in love with her instead while in guise of Linda Lee.Supergirl and Selena repeatedly battle in various ways, until Selena uses her powers to put Supergirl in an "eternal void" known as the Phantom Zone. Here, stripped of her powers, she wanders the bleak landscape and nearly drowns in an oily bog. Yet she finds help in Zaltar, who has been exiled to the Phantom Zone as a punishment for losing the Omegahedron. Zaltar sacrifices his life to allow Supergirl to escape through a vortex atop a steep cliff.Back on Earth, Selena misuses the Omegahedron to make herself a "princess of Earth", with Ethan as her lover and consort. Emerging from the Phantom Zone, Kara/Supergirl regains her powers and has a final confrotation with Selena. Supergirl defeats Selena and exhiles her and Bianca to the Phantom Zone. Free from Selena's spell, Ethan admits his love for Linda and that he knows that she and Supergirl are one and the same, but knows it is possible he may never see her again and understands she must save Argo City.The final scene shows Kara flying up and away into the time-void and returning the Omegahedron to a darkened Argo City, which promptly lights up again.