Tobira wo Akete
Genres: Action, Adventure, Fantasy, Sci-Fi
Type: Movie, Episodes: 1
Aired: Nov 1, 1986
Studio: Magic Bus
Source: Novel
Rating: R+ - Mild Nudity
Synopsis:
In modern day Tokyo, three university students, Negishi Miyako (Neko-chan), Saiki Haruka, and Yamagishi Keiichiro, have magical powers that make them feel like outcasts. They come together one night and are transported to another world. They open a massive door and Neko finds that she is the Princess Neryulla, who must defeat the evil Duran III to free her people. 

(Source: AniDB)