In 2013–14, Stolbova/Klimov started their Grand Prix season with a bronze medal at the 2013 Skate America. After placing sixth in the short program and third in the free skate, they finished fourth overall at the 2013 Cup of Russia behind Canadian pair Kirsten Moore-Towers / Dylan Moscovitch. Stolbova/Klimov won the gold medal at the 2013 Winter Universiade in Trentino, Italy and then took their first national title at the 2014 Russian Championships, scoring 0.45 more than the 2012 national champions, Bazarova/Larionov.