In 2012, Büyükakçay managed to record appearances in the finals of three 25k tournaments in Moscow, Zwevegem, and Istanbul, but lost each one to Margarita Gasparyan, Anastasija Sevastova, and Richèl Hogenkamp. She experienced more success in Fed Cup play, winning three singles and one doubles match for Turkey. Büyükakçay was in touching distance of a main-draw berth at the 2013 Australian Open, but lost in the final round of qualifying to Lesia Tsurenko in straight sets. She reached the semifinals of a 25k event in Namangan but was defeated by Oksana Kalashnikova in close three-set encounter. At the French Open, she scraped past Nastassja Burnett in the first qualifying round, but was soundly beaten in the second by Arantxa Parra Santonja. She would rebound; however, when she reached the final of another 25k tournament in Moscow the following week, finishing runner-up to young Anett Kontaveit of Estonia. She maintained her solid performance for the rest of the season, picking up doubles titles in Shrewsbury, Loughborough, Istanbul, and Ankara.