Tobira wo Akete (1986)

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)