After graduating from the Film and Television Institute of India, Pune, Anuya debuted in the Children's film Mahek, directed by Kranti Kanade. The film was premiered at the London Film Festival and was critically acclaimed. It was nominated in various categories including "Best Picture" at the WorldFest-Houston International Film Festival. She had her major breakthrough in her next film, Siva Manasula Sakthi (2009). Before the film's release, she narrowly escaped from a terror attack while she was staying at a hotel in Mumbai. The film, directed by a debutant, took eight months to complete and was released to positive reviews. Anuya next worked on a film titled Madurai Sambavam. The film was made on a small budget and is set against the backdrop of Madurai. A reviewer from Sify wrote, "Anuya, in a deglamorised role as the fiendish cop who falls for the rowdy is fantastic. She brings so much emotion and reality to her performance and is an actress of substance".
Anuya took a break from films to concentrate on dance during this period. This helped her fetch a role in the film Nagaram opposite Sundar C. After making a cameo appearance in S. Shankar's Nanban, she said that she will not be doing any such roles in future. However, she followed with a special appearance in a promotional song in Naan (2012) and an item number in Nanjupuram.
Anuya is making her Bengali debut in a film titled Gora, based on a novel of the same name by Rabindranath Tagore. As of June 2012, she has completed shoot for the film.